Ahhh, so you're debating the word "completely" here, as opposed to "primarily" or "strongly". Classic strawman tactic.
The point remains, however, that the word "gay" is the defining characteristic of such organizations -- it serves to separate them precisely along the line of sexual practice. There are far too many such groups to ignore the intent.
To affiliate with such a group -- as opposed to something with a name such as Lower Eastern Duluth Singing Ensemble -- is to make a certain statement about one's self. One is not a "singer," one is a "gay singer," and thus the question of self-definition is answered directly.
Surely you admit the obvious.