Many people are OK with it mostly because "the bad people" are targeted (they think, that is, those they disagree with).

If the pendulum swinged conservative in the future and you could get fired for excess "wokeness", the same people would be fuming with rage at the censorship.

Of course the conservative side (which is now all about free speech) did censor others amply when it had the upper hand (from McCarthy to the "parental advisory" stickers and album boycott campaigns from Mrs. Gore - funnily a Democrat, how times change).

Double standards as usual. If you want a free society, defend free speech for those you disagree with and consider "a danger".