I think interrupting is a pecking-order thing. I've come to the conclusion that most rudeness is a nonverbal way for people to establish dominance and hierarchy. This would explain the bristling and overreaction when the person being frozen out or otherwise treated rudely has the guts to protest. It also explains why (some) NTs are rude to one another as well as to NDs, it explains why (some) men are rude to women, (some) adults are rude to children, (some) ethnic and religious groups are hostile to outsiders. (Edit in: it also explains why retaliation is the norm, not the exception, when employees protest abuse, of whatever type, and why such abuse almost never results in serious consequences for the abuser - as in Weinstein, Wieseltier, Louis CK, etc. etc. etc.)
None of that makes it OK, none of that even makes it functional. It's dysfunctional as hell. But if you think of it as ethology (animal behavior, which is true since we are all critters), it may not seem quite so personal. The trick is to find other members of your species who can do "meta" and decide not to play the reindeer games. Easier said than done.
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"I believe you find life such a problem because you think there are the good people and the bad people," said the man. "You're wrong, of course. There are, always and only, the bad people, but some of them are on opposite sides."
-- Terry Pratchett, Guards! Guards!