That makes sense when you consider that in many (not all) cases, censorship is directly tied to a sub-culture's attempt to create their vision of a righteous world.
Inquisition? One branch of Christianity trying to enforce its righteousness on emerging branches and anyone else who didn't fit.
McCarthyism? Attempt to suppress communism to protect the righteous American way.
And so it goes. I think the only modification I would make to what you're saying is that censors are not convincing themselves that they're fighting a righteous battle. They're actually fighting their version of one.
It doesn't look that way from a person outside who doesn't hold their views because we can see that their oppression defines them far better than their values. But a lot of them don't know that. They're believers -- whether it's in the gospel of Jesus, the gospel of Woke, or anything else. And we've known about this for many decades--for differing belief systems to coexist peacefully, people actually have to relax their beliefs and agree that there is a higher standard of human decency that supercedes them. And that is a very tough thing to do when your belief system involves a "true god," or when your political beliefs involve protecting minorities whose suffering has repeatedly been ignored under previous attempts at multiculturalilsm.