This might not be ideal, but I just don’t bother engaging with people where there are deep fundamental differences in terms of basic values or worldview, especially when it’s obvious they’re not interested in hearing anything contrary. My goal isn’t to convince anyone, it’s to find people with whom I already have some shared basis of understanding and reach a point where we can at least understand each other’s perspective.

If I’m truly confident that somebody else is deeply and fundamentally wrong, like creationists or Holocaust deniers or whatever, I don’t take responsibility for their misconceptions and I don’t think I have anything to learn from that person so I just ignore them. Convincing such a person that they are wrong conveys zero benefit to me and is not something that the other person even wants me to do for them. I guess a more positive way of phrasing that is that, when I pick arguments, I do so just as much to give the other person a chance to convince me. If there’s no chance of that happening, it’s not worth my time.