That's a good issue. In my mind, though, you can't really have it "both ways." I genuinely stop caring about people if they act in such a manner that caring about them would hurt me. It's almost tautological, to my mind. I value someone's friendship because it is worth valuing, and then if they insult my music in needlessly hurtful ways, I devalue their friendship. Maybe not in a binary sense from 1 to 0 immediately, but continuously, such that if they needlessly hurt me I assign their opinion a lower impact and the next time they do whatever they did to hurt me, it automatically hurts me less because I care less. Time is all we've got and I choose who I spend mine with very carefully.
For me this is the crucial part. I can't immediately stop caring about someone just to avoid a conflict. It takes place over time, and in the interim you have to have other, more interpersonally-focused strategies for dealing with conflict.Maybe not in a binary sense from 1 to 0 immediately