I concur with the problem assessment: its social function in practice is to assure the group that other people's politics are mindkilled, whereas their own politics are just the normal background.

Maybe not. Only slightly more charitably, they may admit that they get mind killed in political arguments as well. Everyone does, there's no point in discussing it, no one will ever change their minds, etc.

That would be the usual taboo against arguing about strongly held views, whether religion, politics, morality, etc.

I'd emphasize that the phrase tends to only be applied to arguments with The Other, not discussions with Our Side, though logically the other side of the pancake would have the same issue. I predict that a lot of people who use the phrase against political discussion here, still have tons of political discussions with like minded people.

Fundamentally, it's a general memetic protection tactic, that successfully prevents serious encounters with conflicting memeplexes. Christianity has "never argue with the Devil, he's smarter than you and has had more practice in arguing". Other ideologies find similar strategies to keep the Bad Ideas away. The ideas that possess people, are the ones that work to keep them.