Saying the Left are "pro-censorship" is not factually incorrect but definitely has a different connotation.
??
Though surely to say a system or process is 'retarded' means something is holding it back?
To equate this to a derogatory term for a learning disability (worthy of self-censorship!) is, frankly, bizarre and rather smacks of virtue signalling.
Political correctness, woke/cancel culture, whatever you want to call it, is not censorship. And it's not splitting hairs to say this; words have meaning and though 'censorship' is particularly abused, it is still quite different from me looking down on someone who uses the R slur on X (as I do daily)
Wikipedia and the ACLU both use a more expansive definition, where your definition is only 1 type of censorship. The "Left" uses empathy to convince people to self-censor and less often uses "Cancel Culture" to pressure companies into private censorship.
https://en.wikipedia.org/wiki/Censorship https://www.aclu.org/documents/what-censorship
Cancel culture is literally censorship. Deplatforming is censorship. Debanked is censorship.
I don't know what the R word is but there is a group of people you can't even look down at because they have been deplatformed and cancelled.
The left has passed laws and people do get jail time for social media posts in the UK.
For a specific recent example democrat-leaning states had much stricter and longer-lasting covid lockdowns - preventing free association is a form of censorship.