On Thanksgiving, it's usually best if you don't talk politics. The subject tends to aggravate people, and it's very unlikely that anyone's mind will be changed. So don't do it.
But if you must talk politics, how should it be done? A lefty writer I follow is giving the subject some thought. "Every year there's a spate of blog/magazine pieces about how to discuss the political hot potato du jour with your crazy right-wing relatives at Thanksgiving," Kevin Drum writes at Mother Jones. "And every year they're fake. Mostly they provide stock liberal responses to imaginary conservative talking points." (For conservatives, the worry is how to talk with left-wing relatives.)
Isn't there a better way?
Drum is on the right track. He suggests thinking about what your relatives are likely to say and what responses might actually change how they think in small ways. "This would be hard work. You'd have to actually watch Fox News for a while to make sure you know what's really on conservatives' minds these days," he goes on. "Listening to a bit of talk radio and reading some chain emails would help too. And that's not all. You'd almost certainly have to team up with an actual conservative to help you understand both the worldview at work and the kinds of arguments that might appeal to his ideological comrades-in-arms."