I live in a horrifyingly red state. My family is a complete lost cause. Partly because they live so far out in the woods they're insulated from actually interacting with society, and party because they're white reactionaries with heads full of facebook qanon memes and they own stupid small businesses. I'm never winning them over and at best I can just make them confused or angry.

My coworkers are another story. I've had to win them over during unionization efforts. I've never been fully successful, but I've really tried and have won over some more conservative coworkers for impromptu collective bargaining. We've still won over things like PTO and raises, even if we've never been able to get a petition to the NLRB.

Most successful strategy has been keeping them focused enough to forget about their conservative hang-ups. Most conservatives in the US get their ideology primarily from TV news and Facebook memes and thus have very short attention spans. When something practical happens, like a coworker asks them to unionize, it doesn't fit precisely into their reactionary culture war gibberish. So keeping them focused on the practical matters at hands seems to make their stupid meme culture war shit evaporate so long as they're kept focused. Basically, conservatives sometimes forget they're even conservatives as long as their in-group words or issues aren't spoken and their immediate material concerns are the focus.

Part two, if they do start to bring up culture war gibberish, the only technique I've found to work is shame them into shutting up. Get your organizing group to express disappointment with them, or get everyone to tell them their culture war stuff is a waste of time. We've got organizing to do, petitions to sign, we don't have time to talk about how Trump actually won in 2020 or how your kid is brainwashed at school. We're here at work now doing organizing, so get with the picture.

Like that. That works really well if you have at least 5 people all saying the same thing and you bring it up over and over. Eventually they get the message. They don't stop being conservative reactionary fuck-heads, but they eventually learn to shut up. Which is good enough if you're doing something like union organizing.

Part three, this is the less reliable method and depends entirely on circumstances. If the conservative in question knows and respects a person who is LGBTQ, or is a leftist, or an immigrant, or someone else they otherwise hate, they will temper aspects of that particular bigotry. Like if they have a gay relative, or an immigrant spouse, or whatever. They will often have a slightly less bigoted stance, or just keep their bigoted shit inside their own head and not out their mouths. Some of my coworkers respect me enough, and I'm openly non-binary, so during our unionization efforts I could mention stuff I knew would needle them, like how we needed to put in LGBTQ protections into a union contract, and they would nod along. Because they knew they didn't want to piss me off, I was respected enough in their view.

So yeah, that's been my experiences. Probably won't apply to everyone, but hope it helps.