People over-identify their beliefs with their self, so any expressed divergence from their beliefs becomes an existential threat.

This is common with the religious, but not at all limited to them. It's just a human tendency. Buddhists would it clinging or something like that I suppose. It's investment in your own rightness. The most common "tell" is that someone resorts to ad hominem, appeals to authority, diversion and/or moving of goal posts rather than discussion or even rebuttal of your points. This indicates that they don't have facts on their side, other than maybe, rarely, by accident.