I do agree there’s a point past which someone is ideologically unable to be reasoned with. The classic example is neo-Nazis, of course. But also of course, there are redeemed neo-Nazis.
Coming from a conservative family and living in a deep blue state I’ve had my fair share of arguments on both sides. As other commenters have stated, it’s all about emotions. If you can make the other person feel like they are being heard and assuage their fears about X, Y, or Z, then you can make progress, even if it’s small progress.