It's pretty unlikely that any dyed-in-the-wool Republican is going to hear your rational argument and be so astonished at your doctrine that he changes his mind.
I don't think this kind of exercise is that difficult, and I get plenty of practice on HN talking to people who have very right-wing ideas about the economy. But come on; it's not a way of working miracles. You might persuade your uncle who loves Donald Trump to moderate a couple of positions; you aren't going to turn him away from the Republican Party.
This is the main reason that election campaigns have moved on and focus much more heavily on turning out their own supporters than persuading "undecided" voters, who are a statistical nullity.
Is that what's at issue here? I think very few people -- nearly none -- are actually open to being rationally persuaded to completely flip their political beliefs. People with completely different political commitments usually start from different axioms.
That said, few people of any political persuasion are able to engage in that exercise.