I ask them about their views, let them talk without interruption. Show interest as you are trying to understand.
Then I ask some non-threatening questions, build on their answers.
Soon they will start contradicting themselves. Again, don't point it out, just ask more questions. Let them tie themselves in knots.
Eventually, when you actually get a two way conversation going, start gently dropping in comments that reflect your own opinions.
Don't be confrontational, judgmental, sarcastic. Don't talk down to them. Keep the two way line of communication open.
Listen to what they have to say, and respond respectfully. I believe that is what they really want; someone to listen to them.
Works really well for me.
Of course, some of them are just overbearing hateful assholes who there is no dealing with, but most want to connect, to explain themselves. Many enjoy a give and take exchange.
I live in Deep Red Land, but I am usually able to get along with these folks without compromising my own views.
Works for me.