Yeah I was sorta thinking in that direction too.

First take the plank out of your own eye, and then you will see clearly to remove the speck from your brother’s eye

Keep going. Look at Matthew 7:6. "Do not give dogs what is holy, and do not throw your pearls before pigs, lest they trample them underfoot and turn to attack you."

That is (in this context), don't bother trying to give truth (or even have a reasonable conversation) with those who simply will not listen. Zealots, shill, propagandists... it's like talking to a brick wall. If anyone has a technique for getting them to stop being a brick wall and start actually engaging with what you're saying, I'd like to know what it is.

You can call it "transmit only mode" (hat tip Patrick McClure). When you realize that the person you're talking to is in transmit only mode, you understand how the conversation is going to go if you continue it.