I don’t have any direct experience with these youngsters, but from what I have read about them, I would say the professor is correct in calling them a cult. Their behavior, their rigid views, their demonization of those who don’t agree with them, their need for safe spaces, all smack of cult.
The professor himself is an ultra-liberal who never objected to the “Day of Absence” when it involved minorities leaving the campus to show how much they would be missed. He objected because, in this year’s version, WHITES were asked to leave, not to show how much they would be missed, but as a kind of collective punishment for being white.