I wasted 6 hours arguing with a libertarian. But I did succeed in arguing him into submission, where he started accepting that his worldview is wrong. His only defense of himself is that "I haven't read anything about objectivism, I think they might prove property rights and markets there..."
I should probably get a real life.
I think that's the opposite conclusion you should come to. If his ideology is an incoherent mess, that's more a sign that he has no interest is forming a coherent ideology and just wants politics to validate his vibes about the world. He will likely always be incoherent because he has no interest in coherence. If anything I've seen more success changing people who could actually articulate some sensible logic to their misguided beliefs, it shows they have some actual interest in logic.