I don't know what it's like in the states, but I'm very glad gay rights stuff and feminism have been kept separate in the media from what I can see (other than the obvious lesbian feminist stereotype), for the gay movement's sake. Before I found reddit I never knew they were so fully interlinked, honestly my feelings when I see or hear "lgbt movement" have changed. I still support equal rights for everyone, but I don't like being an enemy of a movement I want to support and have my support (and the support of anyone else who sees sexism and gender norms as bidirectional - because it's nothing to do with gay rights) accepted rather than actively rejected - it's hard to feel love for a movement which hates you, completely wantonly. I know it's just a portion of especially vocal and active people, but they are also the ones who are accepted as speaking on behalf of all gay people.

As an aside, one depressing thing I saw on facebook was a gay guy I hung out with in college attended some lgbt in tech talk and saying posting "lesbians have it worse because they are both women and homosexual" despite the fact that the worst homophobia has always been directed towards gay men. This plays into Warren Farrell's idea of yes, women having a social glass ceiling, but men having a social glass cellar - i.e it's better to be a man at the top, but worse to be a man at the bottom. The result of this being that it's actually the men and boys of marginalised groups who suffer the most marginalisation and victimisation (racism, classism, homophobia etc.), I think there's significant evidence for this, but it of course goes completely against the logic of intersectional feminist theory.