You learn how to articulate more nuanced positions. Pick something like, oh, say, foreign policy. Now drill down to a topic. Say, Russia’s involvement in Syria. Read all the facts on the ground and develop your opinion on it. You can now run circles around any nutter just spewing out talking points. On that one topic.
Your job isn’t done yet. Now you have to learn how to have a non-combative discussion. Read the talking points if you like beforehand so you know what they’re going to say and develop counterpoints using your nuanced understanding of the issue.
If you’ve studied the issue enough to come to broad, high-level conclusions that the other person can understand, and you are able to articulate them, and avoid the pitfalls that people normally fall into, (a big one is getting sidetracked onto issues that you don’t have deep knowledge of) then you can win one and exactly one debate with them, without making them feel like they’ve lost it. That last bit is very important.
OK, so you’ve done all that, are you done? No. If you want to make lasting changes on how they see the world, you’re going to have to repeat that performance. Study another issue, learn about the world, do better than the talking points. Rinse, repeat until you have a reputation for being insightful and incisive.
OK are we done now? Not quite. Now you have to attack the hard-hitting issues. The ones people really get up in arms about. Like immigration, or abortion. Don’t try to discuss ‘abortion’ with someone, the topic is so broad the best you can do is talking points. Dig deep and find a particular topic. Never allow a discussion to get general. For every talking point, find a way to drill down to something real.
Do that, consistently, over and over again, and you have an outside shot at getting an unsophisticated person to maybe do a little Googling before spewing his nonsense.
You didn’t think politics would be that easy, did you?