Well, I suppose you have to have some divisions in your choice of music - Christians and Jews and Moslems probably won't have too many hymns in common, but maybe there are a few that they can all sing together.
Within Christianity, there is a distinct division between progressives and fundamentalists, but there is a large majority of moderates in the middle. I think there are a lot of good Christian hymns that express the basic beliefs of that majority. They certainly don't all believe the same thing, but their basic beliefs have very much in common, and good hymns should bring out that commonality and unity.
And yes, I think there's such a thing as sound theology that isn't an impossible goal to achieve. During Lent, the "mainstream" churches in our town spoonsor a weekly prayer gathering that includes, Lutherans, Episcopalians, Methodists, Presbyterians, Catholics, and the United Church of Christ (Congregationalists). Each week, a different pastor gives the sermon - and I've found all of their sermons and all of the music to be theologically sound.
Religious groups should celebrate what unites them, not what divides them from each other.
Makes good business sense, too - the Oregon Catholic Press (now OCP) and the Gregorian Institute of American (now GIA) now market their music to all the mainstream churches.