I try to start all of my conversations about politics or sensitive issues with the question "What would you have to be shown, or what evidence would it take for you to change your position on X?". If the person doesn't have a good answer to that, then they are usually either an ideologue or have not actually seriously thought about the issue in any depth, and it's probably going to be fruitless to try and have a conversation about that subject.
I abide by this rule and can change my views at the drop of a hat when presented with new evidence.