just because the recent right/republicans were able to more effectively lean into the meme-heavy southpark-type (crude, male-targeted) humor as marketing doesn't really track with your last assertion (for me)
On the left, when someone uses a racial or sexist epithet, for example, the reaction is to exert social pressure against that individual. Social media escalates that to a giant dogpile, which, in some cases, results in some extreme cases where the individual loses their job in addition to becoming a social pariah.
However, all of this is merely an exercise in free speech and free association. The person in question suffers no legal consequences for their speech. Instead, it is a large number of onlookers who decide they disagree with the individual and choose to counter him/her with their own speech and/or dissolve any association they have with him/her.
I won't say I condone how little it takes for the crowd to react sometimes or the extent to which they do, but everything is well within First Amendment rights of free speech and association.
In contrast, when something the right doesn't like is discovered, they take legal action. Books are removed from public and school libraries. Laws are written to target anyone who is guilty of the offensive speech (e.g., Florida's Don't Say Gay law). More recently, it's been popular to write these laws such that the offending individuals are opened to civil suits by third parties rather than suffer jail time, as a loophole trying to avoid the Supreme Court striking them down as blatant First Amendment violations.
Not sure it’s correct to characterize that as a reaction of only the “left” - case in point, the reactions to Charlie Kirk’s death.
They handed a guy a seven month jail sentence for posting a joke that Hillary voters could text in their votes.
Saying the Left are "pro-censorship" is not factually incorrect but definitely has a different connotation.
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.
??
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.
I remember taking a California statewide essay exam in middle school whose prompt was specifically to argue for or against banning Harry Potter from the school library. I wrote a stridently anti-censorship piece extolling the virtues of literary freedom and calling out the censorious right for attempting to use schools not to educate, but to transmit catechism.
The essays were graded by (obviously heavily left-leaning) teachers from all over the state, with two teachers independently assigning a score and if their scores differed by more than one grade, another teacher would be tiebreaker.
I got the top score from both teachers--one of only a handful in the (large) school district. I even got an award from the local newspaper.
Now I see the same demographic take the polar opposite view and it's disappointing to say the least. Especially after the "anti" racism struggle session era, it seems to me that their real issue with the book bans wasn't the censorship; they just wanted to transmit the "right" catechism.