To kind of pick apart just one of your examples - anybody running from the Dems to the Republicans because of "censorship" just hasn't been paying attention. I'm not saying the Dems are innocent - they're not - but Republicans have been playing that game, too, and for far longer. The difference isn't that one side engages in censorship (or cancel culture or whatever) and the other side doesn't. The difference is merely that the different sides go after different things and different groups. So the real issue there isn't "censorship" per se; it's messaging or propaganda or voter awareness or some combination thereof, which is a fundamentally different problem to solve.
I would say there's a couple of distinctions though...
Not all censorship is created equal.
First, while it's true that (as you alluded to) republicans have been playing the censorship for a while longer (in general), the targets of republican censorship have fallen into one of two buckets:
A) Censorship targeted at things that members of the Democratic party were also trying to censor at the time (Examples: the Senate hearings pertaining to lyrics and rap music back in the 80's/90's, censoring violent video games, etc...) -- thereby not sticking out like a sore thumb.
B) Censorship targeted at things that the other side would be afraid to publicly counter and defend (Example: pornography, despite the fact that I'm sure many or most democrats are against censorship of porn, no politician who wants to keep his job wants to publicly stand up and proclaim that they're the "pro-porn candidate")
Secondly, the republican calls for censorship have been a little more abstracted (we don't like thing XYZ, so we don't want people to see it), the modern Democratic calls for censorship seem to be more targeted at the individual, attempting to tell them what they can't say.
Thirdly,
the aspects of attempting to leverage private sector proxies to censor for them -- compelling tech companies to do their bidding, instead of doing through the proper legislative process.
Lastly, the retroactive component. (Ex: You told this offensive joke 6 years ago, so we're going to kick up a poop-storm and try to get you fired for it now)
I went back and bolded that third one, because that's the one I think probably puts the most people off.
People can agree or disagree about the level of censorship that should be allowed/tolerated, and to which content they pertain.
But something about the government using backdoor approaches rather than, at the very least, going through the proper channels just "hits different" for some reason. I think largely because when it's done that way, there's no person or court one can appeal to.
Just as an example: Fair to assume you probably weren't a huge fan of DeSantis's "parental rights in education bill", correct?
Now, instead of FL state republicans voting on a bill, sending it up to Ron's desk, and signing it. It instead was handled via the FL state legislature by calling book publishers for legislative panel hearings, strongarming them into not publishing the books by making thinly veiled implications that the publishers stand to lose some tax breaks or abatements if they don't "bend a knee"
That would seem worse, right? There's no appeal process for that, whereas at least when it's done through a typical legislative process, there is at least a measure of recourse, for instance, a group of local school boards and parents filed suit in a district court, and when that got dismissed, they escalated it up to a federal court (which I believe is still ongoing)
The only recourse for the latter is to vote out the people who are doing the strongarming against the companies, in hopes that it alleviates the fears they have about getting railroaded and losing certain protections, and hoping they reverse course. Which could explain why some voted the way they did, and why Muck Zuckerberg did reverse course once the dust settled, and the Democrats aren't holding a majority anymore.