Perhaps part of it is in order to "fit in" with the gay culture that one perceives. Everyone (or at least I do) changes their speech patterns a little depending on who they are talking to, and depending on who they want to sound like.
From a few gay people I've talked to (and my own experience), there is a desire, especially when one is just coming out, to do everything possible to identify with gay culture: listen to campy showtunes, dress androgynously, go to Indigo Girls concerts, get rainbow bumper stickers, address other gay people by the opposite pronoun ("There's Mike -- she looks fabulous!"), etc. The gay accent may be a part of that for some people.