I don't think I explained my last point well. Someone, and it was probably conservatives that started it, turned the gay marriage debate into very much a your-definition-versus-my-definition debate. Very few people I think would actually support eliminating the existence of gay people. But a lot of people would be called to action if they feel that the government is going to define something that is part of their religion differently from their religion. I think "if you don't like gay marriage, don't get a gay marriage" is a great argument. But then people who don't want to bake a wedding cake for a gay marriage get taken to court and lose. If you can understand how people wanting to make gay marriage illegal makes gay people feel like their existence is threatened, it's not much of a leap to see how people in the Bible belt look at that sequence of events as a similar threat. So stop the adversarial nature entirely. The government doesn't get to define your peaceful, consensual relationships. End of story. If I want to not bake a wedding cake, and if they gay community wants to take their business elsewhere? That's the respective individual's business. If I want my next of kin to be a man, or a woman, or neither, or multiple people, that's my business. No one's church stops being considered a church because of beliefs regarding a protected class. No one's getting tax breaks for their relationships that other people don't on the basis of gender. Who can feel threatened?

edit: I'm trying to get away from arguing with anecdotes, but let me share a more extreme illustration of how a Christian might also feel "threatened" since you clearly already empathize with the gay community and why they feel threatened. A while ago the library in the next town over hosted a "drag queen story hour". They explicitly advertized this as being an event for children ages 2-8, where kids could come and read with a drag queen. The library said this was to promote diversity and understanding. Obviously the bible thumpers lost their minds, and the library then pulled one of the performers from the event, citing concerns about that performer being bullied. I googled that performer's name as part of trying to figure out what this was all about. The first thing I found was a video of that person, outside, in public, in a major city, masturbating with a toothbrush. The second thing I found was that person in lingerie kneeling before a Christian statue with what I assume to be simulated ejaculate on their face. This person, using the same stage name, was being promoted by the local government for a children's event. And objections about the appropriateness were labelled as bullying. If you're an otherwise peaceful, church-going person who has not previously been much of a party to any LGBT discussions, do you see why these people might feel like there's a threat to their way of life as well? And why they feel disrespected? There's not a lot of openly gay people in this town. This, and media, are all the exposure any of them gets to alternative sexual lifestyles. I don't know how you come back from something like to a reasonable discussion about the real bullying that happens.