At some point, it becomes obvious that there are people incapable of thinking in anyway that isn't just following a particular herd. That is the point to just decline to continue to participate, and spend your effort on people that are capable of actual thought.

I've found a moment of hope I can share. I can tell you I've now witnessed on more than one occasion such people acting just like you said. I'd encounter them months or years later to hear them debating with someone else and getting it. They then understood.

I've come to realize that in these exchanges that can be frustrating that just because you didn't appear to convince them of something doesn't mean you did not plant seeds that will grow over time and do just that.

This makes it worth it I think regardless of whether I get the instant gratification of them changing their mind.