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Is it "really important that people do not self censor"?
There are many examples of it being a desirable behavior, even unavoidable. Interacting respectfully with people sometimes demands it.
It sounds like some people demand being allowed to say whatever without fear of negative consequences. It sound like demanding that others do not set up minimum conditions for interacting, which is abusive in itself and sets the stage for future abuse.
Some people would benefit from shutting up. Their opinions are horrible and the fact that they do not realize it just makes it worse. Telling them to shut up is actually an act of grace.
Of course, "not self censoring" is wrapped in "against cancel culture" discourse. As in bullies demanding for their violent behavior to be considered part of normal interaction. Which it practically is many spaces. Which is why people are resisting it, which is why some bullies feel like they are being ostracized. Which is true in some cases, and often a good thing.