This is an interesting question for me, because any views of mine that I’m sufficiently convinced of that I’d say I feel strongly about are very basic and I have very few of them. Things like economics and religion are just such incredibly complex subjects that I can’t bring myself to permanent concrete conclusions about them, and at times I don’t understand how other people can. That said I get very defensive when people fail to understand a viewpoint I find relevant, to the point where I will argue said viewpoint as though I fully believe in it. This causes me to get into heated debates with close friends on a somewhat regular basis, which usually die down with both sides making concessions and admitting validity in each others viewpoints, or at least walking away with a better understanding of the other’s viewpoint.
I think this probably comes from the fact that any time I see something I don’t immediately understand or agree with I want to know why I don’t agree or understand. It’s a tendency that’s given me a lot of perspective on various subjects. And because of this tendency, I don’t see how I could ever let a disagreement like that interfere with a relationship I have, because, in general, if I can understand it, I can accept it (even if I don’t agree with it).
I’ve also found that most of the time, differing views, especially when it comes to politics, isn’t so much a difference of basic beliefs or morals so much as it is a difference in the extrapolation of those beliefs/morals. For example: a friend and I once had a heated discussion about reasonable responses to home invasion, one of us felt that force was a reasonable response, whereas the other did not. At the core of it, we both based these views on our belief in the inalienability of personal rights, and while one of us thought that the violation of these rights was such a serious offense that the victim deserved to take any action to protect their rights, the other believed that the other party didn’t deserve excessive response, views which don’t actually inherently contradict.