My own answer:
I am not proud of being white, or straight. But I'm also not proud of being a woman, or having Asperger's Syndrome, per se, because I did not choose those things. What I do feel pride in is the accomplishments I have made despite those traits and the way society reacts to them.
I feel that pride is for things you accomplish, not things you have no control over. So, to me, gay pride or black pride or women's pride is real and laudable, but it's not about feeling proud of a characteristic you can't control. It's about feeling proud of the things you've accomplished in the face of prejudice. And that's why there is no sense in being proud of an uncontrollable trait for which you have never experienced discrimination.