Caught a glimpse of this thread when it was briefly spamjacked this morning, and discovered that it touches on one of my own buttons. Let me therefore add a datapoint and a couple of personal observations:

The datapoint: Both "We Gather Together" and the Julia C. Cory lyrics quoted above ("We Praise Thee, O God") appear in the Pilgrim Hymnal with which I grew up - the copy I have here is a 1965 printing, but the copyright page cites 1931, 1935, and 1958. This was the hymnal of the Congregationalists, subsequently absorbed by the United Church of Christ (UCC).

Regarding searching for/indexing of hymns: my Pilgrim Hymnal has six - yes, six distinct indices:
# authors/translators
# composers/arrangers
# metrical index
# alphabetical index of tunes
# topical index
# index of first lines

This is entirely appropriate, because one of the distinctive things about hymns in the Western Christian tradition is that the texts and the tunes frequently are not welded to one another. The tune indices above reveal a considerable number of tunes attached to more than one set of lyrics, and the body of the hymnal includes several instances of two distinct tunes being attached to one set of lyrics. The melody titled "Kremser" is thus attached to both hymn texts mentioned above, and an Irish melody, "Slane", is likewise attached to two entirely different sets of lyrics. And one text, "In Christ There Is No East Or West", is printed twice, once to "St. Peter" (from the early to mid-19th century), and once to "McKee", described as a "Negro melody" dating at least several decades later. And the metrical index is helpful for determining what tunes will fit a particular set of lyrics based on scansion.

That said... [rant mode ON]

As a writer of both poetry and lyrics (the two things overlap, but don't map one to one with one another), I come down firmly with Joe, above, in distinguishing folk material from verse whose original author is known, particularly where matters of theology are concerned. As long as one is publishing a work and attributing it to a particular author (whether in or out of copyright), I think it's intellectually dishonest to deliberately make changes that alter the character of the work being modified. That explicitly misrepresents the author's intent, and that's intellectually dishonest.

Having said that, let me note that (1) I do *not* object on principle to minor alterations that update language purely for clarity (replacing thou and thee with you and me, or the equivalent, for instance), though I am inclined to keep right on singing the old pronouns myself because for all its dated qualities, the King James Bible is still one of the great works of poetry in all human history, and one ought not fiddle with it lightly. I am of mixed minds as to "inclusive language", having grown up in an era when "mankind" was clearly understood by most people to mean the species, not the gender. (Per the prior note, every newer Bible translation I know makes poetic hash of "and on earth peace, good will toward men".)

What truly gets my goat, though - and the biggest reason I'm now entirely unaffiliated churchwise - is that far too many of the modern alterations have been done BADLY. The UCC's New Century Hymnal in particular is a spectacular hatchet job; at least half the modernizations result in hymns that flat-out don't scan properly. And that's just stupid. (They entirely ruined Lesbia Scott's wonderful "I Sing A Song of the Saints of God", for instance....)

[/rant mode OFF]

Anyway, for me, the Cory lyric does its job right; it's a new hymn, distinct from the old, and is singable on its own merits. The fact that it shares a tune with an older hymn? Interesting, but not at all problematic.