As I see it, "cancellation culture" is to 'political correctness' what the IRA was to Sinn Fein: the weaponized part of a broader entity. In that case the elements were much more concrete, but I think the analogy is apt.
I see 'PC' as a crude, primitive, clumsy attempt to make mutual respect the new Liberal ideal. Perhaps I see it that way in part because I have been focused for some time on mutual respect (of a basic kind--taking one another into account) as the only possible ethic of justice. That is the respect due all human beings merely for being fellow humans.
A requirement of mutual respect follows from a belief in equality: "Equality Is All We Need" here in Medium.
A requirement of mutual respect also follows from observation within material existence: "Real Justice: Goodness without Limit" (also in Medium).