Having have had good conversations with those on the opposite sides of political issues, I know that consciously pacing give and take, making sure the other knows that you know what they are saying, and not expecting agreement, seem to work pretty well to keep things calm, cool, and productive..
Over the years, while making get out the vote calls for political candidates I supported, I had the experience of encountering some number of voters on the opposite side. Instead of saying “thank you and goodbye” right away, I wound up talking with them for a half hour or more and was glad to have done so. I had the satisfaction of learning how people with very different positions approached things. By making a conscious effort to listen to and restate their positions, and then to tell them mine, managed to help keep things pretty peaceful. I also felt that after talking to them for that length of time I had the sense of being a little more personally connected – we didn’t agree on much, but we did agree to talk, and that made it feel like we were sharing some ideas, listening to one another, and not living in separate universes.
At other times not during political campaigns, in hotel lobbies or wherever, I found myself talking for half an hour or more in the same way with people who had very different views, and always felt it was worth the time and the effort. Again, no one was convincing anybody of anything, but we did make a connection, and made a space to at least see where each of us was coming from. I found it useful, and the people with whom I talked also frequently expressed appreciation for the chance to reach out peacefully and reasonably with someone who in some way was from a different universe and had very different positions from their own.