I think this kind of question needs to be addressed on a case-by-case basis.There are the songs about love relationships, in which it sounds a bit strange for a female singer to profess love for "her" (or a male singer for "him") and in which a pronoun or two can be discreetly changed and it sounds fine. I've done that in several cases. Some other songs don't lend themselves so easily to this kind of sex-change operation, and end up sounding awkward or just wrong. Those I just reluctantly shelve, or in some cases, sing them as is.
In this particular case, I'd sing the words as they are. This song is not about men-and-women, it is about people. Specifically, about people singing together. I don't believe it was intended to exclude anyone. The words are really quite powerful, and changing it to "when we all sing," or something like that, I really think waters it down too much. Perhaps a few words of introduction can make it clear to the audience that it is intended to be inclusive.
I have heard this sung in large groups, and it's really great. Has it been recorded?
Cheers, Nancy