This is something my elderly mom struggles with. Being almost 80 and a fundamentalist Christian, she obviously does not approve of same-sex marriage because she sees it as sinful.
If that's all there were to it, it wouldn't be much different than Muslims or Orthodox Jews believing it's wrong to eat pork. They think it's wrong, so they don't do it....end of story, right?
However, the difference between that and my mom's beliefs on same-sex marriage is that
she can't keep her thoughts and beliefs to herself. For whatever reason, she feels compelled to say something whenever she sees a gay couple (or queer person in general) in public or on TV, which in a lot of cases generates responses from the people around her. And that causes her to get upset and start complaining about how "I guess I'm not allowed to say what I think anymore" and "They [LGBTQs] can do whatever they want, and I'm forced to accept it".
That's the same mentality you see here. They're conflating society pushing back against their comments with government forcing them to accept the queer community. I've tried explaining this to my mom, but all she can see is that she's not allowed to say what she thinks and that's just not fair, especially given how "what she thinks" comes straight from the Bible.
So for now I've settled on just letting her know that she lives in a society that will push back against judgmental and demeaning comments about LGBTQs. IOW, it's "Mom you can say what you want, but other people are just as free to say what they want right back at you".
For a lot of older folks it really does boil down to the simple fact that they used to be able to say all sorts of things about the queer community but now they can't, and they don't like it. And to that I say....oh well, maybe just don't say nasty things about other people?