Your question got me interested in best book lists and I noticed Celeste Headlee's book, We Need To Talk, on some lists. She had given quite the TED talk that stuck with me and received lots of comments & views.
So I listened to the audio version of her book yesterday. The YouTube comments that got voted up didn't mention the parts that happened to capture me. One is she tackled the problem of what do you do when you run into someone whose point of view is so opposite yours and repugnant to you, you feel you have nothing in common? One important thing is to be curious. Draw them out to understand how they came to believe what they believe. And show respect. What if you were born into their circumstances? You might believe what they believe too.