No, it's totally fine to dislike her and her music.
HOWEVER, to discredit her work as an activist is pretty questionable from me. She did a LOT for Don't Ask, Don't Tell and NY Marriage. If Obama gets re-elected, I wouldn't be surprised if she starts trying to mobilize monsters against DOMA.
Saying she "exploits" the gay community is dumb. Marketing is not "exploiting." You still a choice to listen to her or not. There's plenty of artists who try to appeal to the gay community and flop miserably. Hating on Gaga for being very good at making a genre/genres of music that a lot of gay men like is dumb.
No I'm over gays acting like she's God. I don't like her. She's too over the top for me. As a gay man I don't owe her anything. Yet her fans will bully others who don't like her. I don't care what anybody says she;s not my cup of tea.
It's never "offensive" to dislike someone if the dislike is justified. So it might be unreasonable to hate her for no reason, but not automatically because you're gay.
Seriously, that logic is beyond silly. Just because someone supports a social issue doesn't mean someone has to automatically gain respect for them. Honestly, I feel she does a lot of harm to the gay community as well, making it seem like EVERY gay guy is suicidal who doesn't feel comfortable in their own skin.
Absolutely not. Not only do gays have a right to dislike her as a musician, but they have the right to dislike her as a person. They might find her personality pretentious, or some gays might be animal activists might no like her meat dress actions or some gay parents might not like her open talk about her use of drugs to create art.