I've had some luck by working backwards to things you agree on, then stepping forward until you start to diverge. You need to be genuinely engaged in their thought process, though, so prepare for psychological damage.
E.g. for immigration, you can start from "this is super fucked up and I don't think we should do it. Why do y'all support it?"
It make take a few "why"s, but I think their reasoning will ultimately end up at:
- Lots of people are struggling financially, that's bad, and we need to fix it.
- Because of supply and demand, having more people in the US lowers wages and increases prices
- If we have fewer people in the US, wages will go up and prices will go down
- There are lots of people here illegally. Kicking them out will fix the fact that people are struggling financially
Which is wrong, but at least is a logical progression that you can challenge. They believe that the social benefits of deporting people outweigh the human costs of doing so. It's "for the greater good" and "you gotta break a few eggs to make bread."
You now get the privilege of talking about the real cause of low wages and high prices being capitalism. You're in your element and should have a DEEP bag of examples. As usual, tailor to your audience, make it simple, and try to avoid trigger words like any -isms.
If you convince them that capitalism is the problem, not supply and demand, then there's no longer any benefit to deporting people and it's only a fucked up thing to do.
They'll have weak, residual arguments like "but they're breaking The Law" or "but maybe it's a little supply and demand too, as a treat?"
At that point, you've won. You can provide weaker pushback on these, and start looking for a way to end the conversation.
There is no world in which it ends in "oh. actually you're right" - our brains take time to change. Your goal is just for them to think about it by themselves.