The problem I have with your post to me and this one is that you're presuming that the other person you're dealing with at the moment shares your belief/perspective/opinion of the issue at hand. What if that person believes that YOU should come to his/her position? Both of you are acting in your own self-interest. Even if the desired results may be positive, there will still be disagreement-and perhaps fighting (literal or figurative)-because both sides perceive their position to be the correct one. That's what I mean by self-centeredness. It is the original sin every person is born with.
" you're presuming that the other person you're dealing with at the moment shares your belief/perspective/opinion of the issue at hand. What if that person believes that YOU should come to his/her position? Both of you are acting in your own self-interest. " Thats a misconception of Objectivism thats common in people who have only the briefest exposure to some of it. Believing that something is in ones self interest does not make it so. Otherwise, Objectivism would be subjectivism. Thats why Objectivists are usually careful to say rational self interest. Its up to us to discover what is in our rational self interest, first through guidance and education but then through observation and reasoning. Opinions vary, but recognizing the most fundamental social values that we should share (beyond the self-engrossiveness that I think you are referring to) is not rocket science.
By the way, theists are just as prone to differences of opinions and conflict, perhaps more so.