A good narrative is captivating. It's really simple and comforting to know that the world is good vs evil and you're on the good side. Those guys are on the devil's side and we must stop them at all costs or it will be THE END OF AMERICA!! ** Dramatic yelling **
It's easy to convince less educated people using fear and misdirection. What are they gonna do? Check the sources and think critically about the topic? Lol
Convincing someone that thinks you're their mortal enemy is difficult.
That's why you have to be their best friend. Show them that you care for their opinion and ask them to explain to you. Show genuine curiosity and then give them something to think about.
"Hey, I see your point man, but I don't know enough about this so I'm not sure. Hey I've found this article that has some interesting points. What do you think?"
It's not easy but I think this is what really creates change
My work has me with people, one on one, for an hour or so at a time. A year or so ago I decided I might be able to help some of my more brainwashed clients start to think for themselves.
The best way to do that, I've found, is like you said. I don't approach the subject like we are two different sides, but instead find points they make that are close to the truth and help nudge them a little more towards opening their eyes. It's actually been pretty successful and it really makes me feel like I'm doing some good in the world.
I don't want them to agree with whatever I think, I just want to to start actually looking at facts instead of going off emotion and bad information.
Hey I've found this article that has some interesting points. What do you think?
Oh, don't read that. That is all just propaganda, you can't let them get you.
-a literal response I've received, many times.
Trying to ask them real questions, like who "they" actually are that are trying to make your life in particular worse, is about as good as I have managed. But on some of the more egregious points, they always seem to think they have actual good serious sources on how trans people are actually all just predators or something. The more attentive ones may even be so kind as to add a "present company excluded"