I am a liberal person who lives in a deeply conservative area (Utah). I have had many conversations with staunch conservatives, some of them close friends and family. One-on-one is different from the one-to-many format, or the one-to-one-in-front-of-others format. It's quite possible to have a civil conversation about such things when there isn't an audience.

I have seldom (probably never) seen anyone have a big change of heart from such discussion, but often both sides concede a little, and it feels like progress toward common ground, minuscule though it may be.