You can't really "change someone's mind" unless they're receptive to it. Quite often you'll just end up in a situation where both parties are already hard set into their position; then they both enthusiastically repeat their best arguments and logic, while completely ignoring what the other person is saying. The hope is that there's a magic combination of words that will trigger the incantation that changes the opposition's mind. There usually isn't.

As a thought experiment, if you wouldn't be willing to "change teams" no matter what the other person says, they probably feel the same way towards you.

I have a family member who is an avid Pauline Hanson / Trump supporter; despite my reminders that those people hate me for who I am at a fundamental level and would see me suppressed, deported, begging on the streets, or worse. I'm "one of the good ones" you see, an exemption to patch over the cognitive dissonance. I would never support them, because it would be literal suicide to do so. I'm sure they have similarly strong opinions about my favourite progressive political parties.

That said, I don't have a good actual solution, and at least arguing about things raises visibility and could sway undecided third parties. But at a certain point it becomes too exhausting to continue arguing all the time.