> The difference is when it's an institution (private versus public schools for example), that's pretty easy to disagree over. One side does not believe the other is inherently evil and a 'lesser' person. When it's about individual rights, and an attack on you as a person, and your inherent rights as an individual, that is almost impossible to overcome.

I think you articulated it far better than me. Certain things I could hardly care what another person says or thinks on the matter. But on certain issues or rights if there's a fundamental disagreement, I find the opposing position not just in direct opposition, but in a way actively working to undermine my position. I can't be friends with someone when there's such a basic difference in values; if we don't agree on that, there might not be much else we agree on.