From the short time I've lived, I've deduced one thing;
Society is stupid, or rather, changes easily to the point they fit into a mold, AKA a stereotype. Say you have an average person who is usually happy, and something tragic happens to him that sends him into deep depression. Maybe they may become an "emo", or develop habits that someone of that stereotype will have. Usually our first instinct upon a problem is finding a way to solve it. Naturally, if I wanted to solve a problem that's happened to others, I would go for the best solution. The best solution though, is usually based on a person's preferences. They may believe following a stereotype will solve things, therefore they join it as a false cure. One of my friends did that a year ago after the death of his pit bull.
The other reason seems to be that someone finds a stereotype with people who have similar traits, and to fit in they usually adopt the rest. I myself did this once while trying to fit in.
Now, this is coming from someone who the only things he knows about psychology is how to trick someone into giving you something, but the way I see it, the reason a homosexual may adopt the "gay" stereotype is somewhat of a want to be around those who will accept them. It would seem that humans, though some claim to be "loners" and don't need to feel accepted, seem to have a bit of a social need to be with others that know how they feel and what they are like. Someone that understands them, so to speak. In a stereotype, it seems to be often to gain most if not all traits of the stereotype if you never had them. A few years ago I went "emo", but it didn't last long because there wasn't anyone around like me and I became more of a social outcast than I already was, if that's possible.
TL;DR, My opinion is some of the homosexuals that think they should try to fit in with the homosexual stereotype subconsciously begin adopting the accent.
Then again this is coming from an asexual who really doesn't know shit about psychology. I wouldn't count on this for an answer.