This is spot on and something I teach in social psychology. One thing that helps is increasing membership in other groups so that the dismantling of one group doesn't fracture their self identity. Granted I usually teach this with more benign examples (e.g. if you're a "good student" and get a bad grade, it hurts more depending on how important it is to your identity). But the idea is the same.

A few things you can look up though: cognitive dissonance, confirmation biases, contact hypothesis, and probably a few more. The funny thing is, social psychology as a discipline boomed after WW2 because people wanted to know why Nazis were Nazis. It's only recently we also realized that social rejection uses the same parts of the brain as physical pain, though.