Hate towards beiefs is fine, and I think you’d even agree with that. Would you agree it’s bad to believe that a subset groups of people should be removed from the world? I would hope you agree that that is a bad belief and doesn’t need to be accepted.
But it’s also missing the point. Being gay isn’t a belief, it’s just the way someone is - just like race, just like gender. It’s not a belief like a political stance is.
They’re two different things and it’s not hypocritical to treat them differently.