It's always good to keep the conversation going, even if finding some sort of middle ground seems hopeless. That's why diplomacy and more diplomacy and even more diplomacy should be engaged in, rather than war. For example, the little pipsqueak who runs North Korea is certainly an irritating presence, but is eliminating him worth your son/daughter or your grandson/granddaughter? Probably not. So we need to try to keep that conversation going.
As far as the conversation between believers and non-believers is concerned, I find that I have always had close friends on the other side, in both politics and religion. I don't find it hard to have a relationship with those with whom I disagree. One of the tenets of my faith is that everyone is a child of God, even if he/she is not of my religion. I think Jesus was on to something when he said to love your enemies and to pray for those who persecute you. That sly dog! He realized that once you pray for an enemy, he's really no longer your enemy. From Native American wisdom is the advice to walk a mile in somebody else's moccasins before you judge him/her. That's good advice.