I've become increasingly cynical on this topic and now generally feel that political discussions with partisans is almost entirely pointless. There's a ton of psychological baggage holding them to their views and it greatly outweighs any amount of reasoning you could do.

I think because libertarians care so much about the ideas and the philosophy it can be hard to grasp that basically no one else cares about that stuff. Discovering an inconsistency would probably keep us up at night, but most everyone else forgets about it immediately.

All that said, I always give people a chance and if they're open to dissenting views we can have a nice conversation.