I think there are many factors in deciding whether to edit hymns, and there are usually good reasons to take a conservative approach, i.e., if it isn't broken don't fix it.
Religion loves tradition
Religion is extremely conservative in the way things get done; I'm sure there are hundreds of resources out there examining the significance of this so I'm not even going to try, except to say that people like to have traditions and formulae. It is comforting to follow a prescribed ritual. To some people there is great value in being part of a culture and community and tradition of worship that dates back centuries or millennia and connects them to generations past and retains the profound and only incorporates the best innovations, etc. I have family members who feel especially strongly about this.
People get attached to the versions of hymns they grew up with and the specific translations of liturgy and musical settings used for different parts of a service. I grew up with particularly somber and spooky Fraction Anthems with certain English translations from the Latin; I heard the same ones nearly every week for about 15 years. There are plenty of other translations and musical settings out there, many used by other congregations within my own denomination. But now any other version, even the same words to a different tune or vice versa, is extremely jarring and I feel (irrationally) cheated out of a part of the service I like and anticipate.
For this reason people will resist arbitrary change within the service, including updates to hymnals. You'll need to justify any innovations you make, even minor ones.
Language evolves, but that doesn't mean we need to update older but still intelligible language without good reason.
In the past century there has been a backlash against flowery language and convoluted manipulation of the language for the sake of meter. We Americans are generally not taught to write in tight metrical schemes, to write lyrical prose, or to value either as a contemporary pursuit. Now, when we encounter it in older poetry or hymns it feels foreign and artificial.
But we can still understand it. Often, with just a little training to get past the unfamiliarity of certain conceits, we can appreciate the beauty of it. Sometimes it even encourages closer reading and deeper contemplation of the meaning of the text, especially when you get away from idioms that have become so cliché that your mind glosses over the literal meaning. (I think it's unfortunate that people don't spend much time exploring hymns and prayers that way, they just read them aloud in church; but those efforts usually go into Bible Study exclusively.)
Once the meanings of words and phrases no longer retain their meanings enough to communicate effectively, then there is a problem worth solving. For instance, I feel strongly that it is good to have a Bible translated into a language you can understand. It makes sense to release new translations or editions when the old one no longer functions as well as it once did because the language has changed, or when new scholarship reveals mistranslations.
But translating or editing a text that matters to people is a big, gnarly can of worms. Check out all the competing translations of the Bible into Modern English that are available: Modern English Bible translations. Scholars, churches, and political factions can get extremely contentious about even the smallest details, and with good reason. In the case of the Bible a translation decision even over a single word can reshape the worldview of millions of people.
Like the Bible, hymns are products of a specific time and place, and they are evidence of a mode of worship shared by that author's community and culture. The specific word choices have value beyond the literal meaning; they are clues into the minds of the worshippers who originally wrote and used the hymn. (Psalms are actually just ancient hymns!)
There are lower stakes and different factors in translating and editing hymns for a congregation to sing.
First, these are not primary religious texts, and everyone understands that they are tools for worship and not so much instruction for what to worship. That generally gives you a bit more editorial and artistic license.
Second, a major factor is figuring out whether you are dealing with a specific original text in your hymn, vs. a traditional song whose original authorship is unknown and to which many sets of alternate lyrics exist, vs. a translation from a Psalm, vs. a translation of a hymn from a different language.
While some are traditional songs whose authorship has been lost and whose lyrics have evolved organically over time, many are poetry attributable to a specific person. In these cases there is usually one author who has penned the lyrics and there exists one authoritative version. If it was in English it is usually still intelligible to the people who will be using your new hymnal.
For instance, here's a hymn by John Milton that is 400 years old and which was in the hymnal I used growing up: "Let us with a gladsome mind"
It's old, but the meaning is still clear. Moreover, it is part of a particular author's oeuvre. We don't usually do new, Americanized editions of Shakespeare, or the prose writing of Jane Austen and Charles Dickens. It could be perceived as somewhat disrespectful to the original work, and many people would argue that modern readers should just devote a little more mental energy toward appreciating old but still high-quality writing, particularly when it remains associated with its creator as a bit of intellectual property.
Most common hymns in English originated in English, but some are translations from other (usually European) hymns, and here you might claim much more latitude for interpretation, correction, retranslation, etc. (For an example of this, see two English translations of the French Christmas carol "Un flambeau, Jeanette, Isabelle": "Bring a torch, Jeanette, Isabella".) With Psalms, you can have translations that work lyrically within English without veering much off of the original meaning, or you might make the editorial decision that it is okay to use a more liberal translation of the sentiment rather than the specific metaphors. Of course, you might consider one translation to be so old and so common as to be the authoritative or traditional English version and therefore be more cautious about making changes to it.
Lyrics to hymns are poetry.
Lyrics to hymns are traditional poetry. They must fit a meter and rhyme scheme, and they are artistic works. Therefore the authors take poetic license with the language to make the words and phrases fit. A lot of the features that strike us as a bit odd today were incredibly standard ways to handle meter, such as DancingDino pointed out (e.g., marking blesséd or other past participles that way is a standardized way tell the reader/singer that it should be pronounced with two syllables, but is never used or needed in prose writing, and elisions are used to force something that could be pronounced with two as one syllable, such as "o'er"). We don't write metrical poetry much, but as far as I know there haven't been new "standard" conventions introduced for this.
A tangent: You may notice that (in many hymnals at least) at the bottom there is usually some fine print about the author of the lyrics, the musical setting, "translated from the French," etc. Sometimes they are poems set to music by a different person, as in the hymn above. Sometimes you can even find multiple settings for the same poem. (Why? There are certain simple meters that are especially easy to sing as hymns, and lyrics and tunes can be swapped out. For more on common meters, see Wikipedia's Metre (Hymns).)
Summary: when are editorial changes to hymns okay?
I think there's a case to be made for updating and editing hymns because they are meant to be tools to enable thoughtful and sincere worship that reflects the values of the denomination using them. However, the reason to keep antiquated hymns around is the same reason that it is important for the editor to respect the tradition and the history and the literary value of the hymns by making changes only when they are truly justified.
I think that it is usually fine for an editor to update spellings if the meanings have not changed and (some*) punctuation for clarity. This does not substantially change the lyrics.
It is not advisable to mess with any metrical decisions (* leave the elisions and accents alone) or the lyrics of anything with strong attribution, because you are interfering with a specific author's poem.
If the lyrics of a traditional song or a translation no longer convey the same meaning, you may justify modifications. (Always best to indicate that a work has been edited and to cite the source from which the previous version was borrowed.)
S. Mitchell made a good point about more radical changes to match the values of the people assembling the hymnal-- this kind of thing you may want to discuss with theological authorities in your congregation or denomination before publishing.