This is partly a personal rant, but I know I'm not the only person to get burned by irrational people sucking my effort and frustrating me only to reveal I was completely wasting my time (if your reaction on reading that is, "Well maybe they frustrated you because your arguments weren't valid", then you haven't been burned by irrational people enough times). So I think there's at least a chance that someone will read this and be encouraged by what I say to give up on hopeless things and focus on more worthwhile things.
For many years of my life I've thought when going into arguments with irrational people, "I know he has an emotional incentive to be irrational on this issue, but surely if I'm patient and refute all of his arguments in sufficent depth I can make it impossible for him to deceive himself". But I gradually learned something: the reservoir of objections is literally infinite. Someone can always raise another objection that sounds reasonable if you don't read the entire context or aren't trying to rationally evaluate it and just want an excuse not to believe in something that would shatter your worldview. And of course, as the length of the context grows it becomes easier to forget about the first couple objections that were refuted and begin recycling them with variations of the word salads.
No claim is ever sufficiently proven to someone who does not want to accept it. So we need to learn to give up on people.
I'm one to talk. I still haven't learned the lesson I'm trying to teach. I still sink time into wastebins regularly, even though I know intellectually that they're wastebins, because I just can't resist the pull of the false hope and the feeling of superiority.
There are still valid reasons to argue with irrational people. Mostly if you do it in public, you stand to make a bad person look like a total retarded moron and thereby maybe, maybe, sway someone else who will listen to it at some point. Or just damage the reputation of somebody like that so they have less of a following to spread their violent ideas to.