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.
My family became very Anti-Vax during that time. My wife and I had just had a newborn about a year in to the pandemic and demanded everyone get their vaccines before they got to be around the baby.
My parents didn't get any and didn't see the baby for a while.
Then when we did start seeing them, they had completely lost their minds. Blatantly racist, blatantly homophobic. Even when it wasn't things political, it felt like they had forgotten how to properly talk to people in an appropriate way. My mother made comments about my DAD having relations with my wife and that the baby wasn't mine.
I know they watch Fox, I know my mother watches a bunch of far right-wing YouTubers. All of it has led to them barely being functioning adults.