Historically, censorship is not a right/left dichotomy. Tipper Gore was big into censorship and it definitely cost her husband votes in 2000.
However, let's look at the states that have passed laws effectively banning pornography: Montana, Utah, Texas, Arkansas, Missouri, Mississippi, Louisiana, North Carolina and Virginia, with Arizona and Kansas having bills coming up for vote.
Of these only Virginia had split control between parties in the legislature (at the time the law was passed). All the others had one particular party in control of both chambers.
Now, I don't mean to imply that this is an entirely one-sided issue - it isn't - But just because both sides are bad doesn't mean that both side are equally bad.
I think framing it as right/left is a bit... I don't know, it's not a good way to discuss it. What we are seeing is a rise in authoritarianism (worldwide) and, in the US at least, one party has gone all in on authoritarianism while the other just dabbles in it.