> The only thing, why do you assume that only people "on the left" could be intrested in using these tools? Sure it's people "on the left" that are creating them and control them now
Your critique is correct, the right is every bit as brutal about censorship when it comes to a context of authoritarianism. The left in the US is progressive (to varying degrees) in mentality, adopts technology much faster, and gets to utilizing new tools (in this case online) for censorship much faster accordingly.
The interesting thing about the left in regards to censorship is two fold: they (used to) pretend to be the champions of free speech and civil liberties, that makes them a dangerous fake protector. They can strip your civil liberties much easier, as their own base will remain quasi-silent (as we saw in the Obama era), while the right often won't protest because they agree with the abuses. This is fundamentally why the left was able to put us into Vietnam: there was nobody left to stand in the way of it, the right (more inclined to war) was naturally going to agree with the premise.
They're also fast adopters of technology. In my opinion people in the more left half of the political spectrum (call them Democrats or whatever makes sense), on average, move substantially faster as adopters of technology (Clinton & Obama were far more technologically progressive than the Bushes or Trump). The big platforms are all extremely left in their political bias, deriving from the people who work there, the memo was correct in that regard - not to mention credible people like Marc Andreessen and Peter Thiel have noted this publicly for years. These platforms are/were built by young people, who (likely inherently) do not tend toward conservatism.
It makes perfect sense that social platforms founded by people with a left wing bias, including: Twitter, Reddit, Facebook, Google - would then link up with left-favoring ideology/politics/causes when it comes to what they allow on their platforms, or what ideas they tolerate.
The left are the fast(er) adopters of technology, at least in the US. Of course they're going to get to using these tools for censorship before the slow-moving conservatives do. The far more scary part, is when the right catches up, and both sides are gun-ho about abusing technology for censorship.