The Left have always been a bit more 'censory', generally because of their bleeding hearts on behalf of the minorities that are the targets of the Right's exercising of their free speech.
Such is my understanding. I don't really mind either stance, with the caveat that anything 'censory' has a chance of having it's definitions expanded (and admittedly, this is succumbing to the slippery slope fallacy).
> The Left have always been a bit more 'censory'
Not "always", and not even now. It's always contingent and situational. Same goes for nearly every clause in the Bill of Rights.
At various points the left has been associated with the fights against obscenity laws, against Cold War loyalty oaths, against blacklisting, against bans of books.
At various points the right has been associated with the fights against desecration of the American flag, against the teaching of human evolution in schools, against depictions of sex in media, against anti-war demonstrations.
But I think both "the right" and "the left" are kind of reductive and caricatures. I guess forcing you to go in a camp is one of the great woes of American politics.
100%, it only seems to fuel the already-present tendency for tribalism.