I don't think you need to, and I don't include it. Racism is learned, and often by association with something not caused at all by race (like poverty, and poverty that leads to crime).

Studying racism in sociology (my sister was a sociologist), there are strong indications that "racism" against any visually identifiable minority, across many countries and many centuries, is highly correlated with poverty, lack of education or illiteracy, poor use of the native language, and the low level of jobs the minority is required to work. This holds true even for migrant groups when there was no noticeable racism against the minority before migrancy increased. But once it starts, racism can be a self-perpetuating cycle; the minority cannot get decent jobs, so every generation is mired in poverty, lack of education and low level jobs (even if they gain fluency in the language).

I'd leave out racism. The purpose of children's books is entertainment, you don't have to teach them anything. They want the same thing as adults in their fiction, although it needs to be slightly easier to follow: Adventure, heroics, and an exciting story, and mystery, and magical powers. They turn the pages for the same reason adults do: To see what happens in the next few pages, and in the next chapter, and at the end of the book. (All three of those simultaneously).

The purpose is NOT to teach them about X,Y,Z or racism; the purpose is NOT to show them the pain and despair and injustice of the real world. That is what they are trying to escape! The purpose is to entertain and make them feel their hero triumphed against the odds through her brilliance and skill, with the help of the friends she would walk through fire for, even that irritating boy.

It's okay to be dark, Harry Potter proves that. But racism is pretty much irredeemably dark and it is not a darkness one can overcome. The hero can defeat a villain, or a crew of villains, but she cannot defeat a billion racists in the world. Even in a book like Harry Potter, you need a happy ending, and if you introduce them to the issues of racism you aren't going to have one. And you will alienate the majority of potential readers, because they are either minorities that have experienced racism, or people that are not minorities but despise racism.

The point is not to reflect the real world. The point is to entertain people, and I see nothing entertaining about racism.

Racism is a real thing and likely a real issue that your audience may come across.

Even the likes of Harry Potter dealt with this kind of bigotry, as do a lot of fantasy franchises. Harry Potter had blood statuses, Lord of the Rings had animosity between elves and dwarves, Star Wars (in the non-canon Legends, at least) dealt with unfair treatment of various alien races. Where differences exist in the real world, you can expect a form of bigotry to exist also. It's a dark part of the human condition, but it's one that can be addressed to kids in a tasteful manner, and dealing with the human condition, even in stories about aliens/robots/whatever, make your characters a lot more relatable to the reader.

So should I use racism as one of the parts of my worldbuilding? Or write a story without racism as part of my worldbuilding?

Yes, you should add racism to your worldbuilding. Wait – hear me out.

Racism is real, and it's an "ism" – I mean, it's a society-shaping force. Racism is not neighbor squabbles between an elf and a dwarf. Racism shapes the tiers of society, and the geography of neighborhoods. It is woven into the schools, the politics, the national identity, and the fairytales.

Racism is why maidens are "fair", pirates are "swarthy", and gypsies sleep outside the city gates. It is defined by a power imbalance that is maintained through institutions, curfews, the legal system, who gets to be mayor and who is a servant, which religions are pushed to the fringes, and taxes on foreign spices at the trade market.

Your story doesn't have to be about race, or acknowledge racism as a theme. But in nearly every fantasy adventure you'll have a "Dorothy Gale" stepping out into a strange world. That world has structure: haves and have-nots. People with power, and the underclass. This is not topsy-turvy power. There is a clear oppressor and an oppressed. Tigers and bunnies. This power dynamic is never reversed.

It stays that way because the oppressor race is – ongoing – decimating the oppressed by imprisoning their leaders, robbing their workers, and marginalizing their children. You'll have pockets where the structure is strictly enforced, and other geographic areas where the structure is relaxed but not reversed (tigers and bunnies co-existing, but no bunny-eating tigers). It is the "terrain" of your society.

What you don't want is racism just to justify racist characters: the Southern sheriff, the Nazi commandant. That's a self-serving loop. It will always feel "preachy" and artifical.

What you do want is racism that creates a ghetto and an opera house, banks and slums, all in the same city. You want the kind of racism that gives your characters terrain handicaps. It's not enough that they go to exotic places, they should experience situations and reactions that de-center and challenge them. The storyworld is at least equal to, if not greater than the character in importance to the stakes.

They stick out, they don't know how to behave, they need help from wary locals. But also they are treated unfairly, misjudged, and run afoul of authority. Maybe they witness injustice, or get unearned glory. It forces them to adapt and grow, and teaches learnable "rules" for the world. This makes your worldbuilding relevant to the story. It offers plot points and narrative obstacles.

Since Star Trek was mentioned, remember it was the utopian ideal in-world, but also this was a fresh take at the time and it was almost like a UN mission. Everyone from different countries. I think the current cliché is the 2 warrior enemies who form a respect on the battlefield, but none of these acknowledge the real power dynamic of how racism works, and continues today. You don't have to solve it or necessarily build your story around it, but ignoring racism is going to be like ignoring physics. It depends on the story you're telling and how realistic/escapist you want it to be. You say "dark" so, I don't see how you gain by pretending it doesn't exist. You are not writing utopian Star Trek. You should add racism, and allow it to inform the world you build and the story you write.

Maybe not Racism, per se...

Any group of sufficient size is going to exhibit patterns of tribalism. That's just how humans are wired, and it shows up in even the most tolerant of societies. Tribalism taken to an extreme can manifest as racism or nationalism, but even mild tribalism is often conflated with racism, whether intentionally or not.

I think not acknowledging that tribalism is a natural tendency of humans would remove a dimension from your world. Feel free to ignore it if it gets in the way, but it can certainly be a hook to help drive your plot and create interesting dynamics between the characters, as well as directions for character growth.

So, should you include racism in your story? You have a lot of groups in conflict, and they're probably going to have a lot of hostility toward each other.

By the way, if you find this post useful, copy and save it before it gets downvoted and deleted.

If you accept the definition of racism as a belief in innate qualities which make different races or groups inferior or superior, I wouldn't bother with it unless that belief is a specific part of the plot or a character arc.

If you consider racism to be the disliking or hating a of group for whatever reason, then you're going to have to include it, because if you don't your story will probably be a painfully unrealistic rose-tinted utopia that could very well insult your reader's intelligence.

It is completely reasonable for characters to have negative opinions about groups whose members have harmed them in some way, even if these opinions are inaccurate generalizations.

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Break free of the thought restrictions that others are trying to force onto you with their ideologies and social demands, conventions and norms that they enforce with spastic rage and unwarranted shaming.

Then, use your own logic and intellect to determine how the people in your story world would reasonably think, feel and act according to what they've been taught and what they've experienced.

Then, ask yourself: What is racism?

The belief that all members of each race possess characteristics, abilities, or qualities specific to that race, especially so as to distinguish it as inferior or superior to another race or races.

This next quote is from the same definition, but it better defines actions motivated by racism.

Prejudice, discrimination, or antagonism directed against someone of a different race based on the belief that one's own race is superior. ‘a programme to combat racism’

Source

Bear in mind that racism is a belief.

Now consider prejudice.

noun An unfavorable opinion or feeling formed beforehand or without knowledge, thought, or reason.

Any preconceived opinion or feeling, either favorable or unfavorable. unreasonable feelings, opinions, or attitudes, especially of a hostile nature, regarding an ethnic, racial, social, or religious group.

Source

Racism is a belief. Prejudice is an action. Prejudice is an internal mental action, a thought, but it is still an action. Discrimination is an external action where someone discriminates against another person.

Now that we have some definitions, here's an example:

"Elves are naturally excellent archers."

This is a racist statement because it attributes a skill to a Elf because of his biological heritage, his race.

"Elves are excellent archers."

This is not a racist statement, because it doesn't state that Elves are excellent archers because of their race. The statement is a generalization, because somewhere there's an Elf who's an incompetent archer, but the statement is not racist.

"Elves are excellent archers because they're trained from birth."

Again, this is not a racist statement, because it states that Elves are excellent archers because of their training, not their race.

This belief that Elves are excellent archers, whether it is racist or non-racist, can cause racial discrimination:

"Nay, Willfire, you cannot join my elite troupe of archers, for you are not an Elf."

The person denying you admittance to the archery troupe is 1) prejudging you, because he decided you aren't as good an archer as an Elf without even seeing you shoot, and 2) discriminating against you because of your race, because you are not an Elf.

The notion that 'Elves are excellent archers' is also a stereotype.

Stereotype:

: something conforming to a fixed or general pattern especially : a standardized mental picture that is held in common by members of a group and that represents an oversimplified opinion, prejudiced attitude, or uncritical judgment.

Source

So we've nailed down definitions (to paraphrase):

Racism: The belief that races have innate qualities which make races inferior or superior to each other.

Prejudice: To form an opinion before having the facts or a decent amount of information that would enable one to draw a reasonable conclusion.

Discrimination: To treat someone differently because of a reason not related to their merit or qualities relevant to the issue.

Stereotype: A standardized oversimplified opinion or uncritical judgement (a judgement without looking at the specific facts).

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Now let's take it to your story.

You have a lot of groups in your setting: Native American, Viking, English, Irish and Greek. These groups are probably going to be in conflict, and therefore they may not like each other very much.

Consider what the characters in your story have learned, both from what they've been taught and from what they've experienced. Look at the world through the perspective of each character.

A character who has lived through a Viking raid will probably think Vikings are bloodthirsty murderers, no better than ravening wolves, and so Vikings should be put down like wolves.

A character who was pushed off of his land will hate and despise the group that did it, and form unreasonable generalizations about them, like they're all heartless greedy exploiters.

A character whose home is destroyed and ends up as a vagabond falling in with a group he previously feared can discover that while that group can generally have fierce warriors, they also display love, affection and honor. The character can come to understand there is good and bad in that group, even while struggling with his grief and desire for vengeance. Or the character can reject it, and stick with the conviction that they're all killers deserving of being killed themselves.

Note that the character's intellectual conclusions and opinions often serve deeper motivations. The character wants revenge more than he cares about facts, so he sticks with conclusions which make it easier for him to seek revenge. See what I mean?

You as an author must be aware of race, ethnicity, sexual orientation, disability, and other issues that exist in the real world. You as a person need to be aware.

How (or if) you depict these things is up to you. But it needs to be an informed decision, one where you decide how best to deal with the issue.

Some authors make their entire world lily white and ignore all issues of race or racism. Don't be like that.

If your story is set in the real world (past or present) then, yes, racism is a part of that world. You can show it directly or not, but don't write as if you're unaware of it.

If your novel is set in the future, an alternate Earth, or another planet, then issues of race will be potentially very different. Humans as a whole make distinctions and then rank them. I don't know any society where that never happened. Race isn't always one of those distinctions (and in places where there is only one race, as we would label it now, ethnic distinctions may or may not be a factor). There will always be something. Gender and social class being popular choices.

Look also to your source material. How does it deal with issues of race? If older mythologies, it might not deal with it much, if at all, though people of the world interacted a lot more than many think.

How does your source material deal with difference? In what ways did they classify, judge, and rank people? What about people not as individuals but as members of groups? Groups they were born in to and can't change?

If your book is already dark and has elements from a wide diversity of racial and ethnic groups, it would be odd not to include racism, even if it's something that happens outside the story.

There is more than one way racism can be present in a work.

For example, when Star Trek have on the bridge of the Enterprise an Asian pilot, a Russian navigator and a black Communications Officer, and they all get along swimmingly, all at the time of the Cold War, the Yellow Peril and the Civil Rights Movement, the show deliberately confronts the viewers' perceived racist expectations. Racism is present in its conspicuous absence. The show speaks loudly on the topic by showing racism not being there.

In one episode, Star Trek chooses to speak about racism in a more focused way: a fellow officer accuses Spock of being in league with the Romulans, on the basis that he has pointy ears like them. This trope is called Fantastic Racism. That allows one to talk of racism by way of a metaphor.

Finally, you can highlight actual real-life racism. For example, in Naomi Novik's Spinning Silver, a story about a Jewish girl in late-medieval Lithuania, anti-Semitism is very much a part of the story.

Now that we've established that,

What serves your story best?

Does your story even have different "races" - different ethnicities, or different sentient species, or whatever? Is there anyone to be racist towards?

Does racism "belong" in your story?

There is no Jewish character in All Quiet on the Western Front, even though Jews fought on both sides in that war. Nor are any other "races" represented, or mentioned, and so, there is no racism or conspicuous lack thereof. Because that particular issue is not part of the story Remarque set out to tell in that particular book.

There is no racism in the Amber Chronicles, because the Princes of Amber treat all humans as "subhuman" compared to them. Again, racism doesn't "belong".

To quote myself, your story should contain all the elements that it requires, and nothing but the elements it requires. "Including" racism, or anything else, that isn't useful to the story in any way is called 'shoehorning', and is not a good practice.

Is your story served in any way by some of the characters experiencing or engaging in some form of racism? Does it add tension where tension is required, does it set up some theme you wish to explore, does it do anything? Then go ahead and include it. If it does nothing for the story, then don't.