That's exactly right. They are using the quaint puritanism of US (porn is bad) combined with the growing anti-free speech sentiment of the modern left as a vehicle into introducing mandatory censorship mechanisms into online platforms.
We on "the left" are not "calling for" the banning of porn or "mandatory censorship" of it. Nor are we puritans.
In fact you can probably thank "the left" (again, eyeroll) for the liberalization of sexuality in the west. When "the right" was "in charge" it was an era of sodomy laws, anti-pornography "decency" etc. Mostly struck down by liberals.
Expecting ethical and legal behaviour around consent and people's private rights to their bodies and images of their bodies is not censorship or puritanism. It's not "left wing" either -- it's fundamental small-l liberalism.
Dear god, I'd expect libertarians of all people to be up in arms about the private property rights and violated individual liberties of people having their personal bodies and sex lives sold against their will. Somewhere Locke et al are spinning in their graves.
This is not some left-vs-right partisan issue.
In any case the Biden White House has already created a disinformation board and has coerced and pressured private social media companies to censor for them or face penalties and regulation.
Yes, it is a partisan issue, actually a bipartisan one, where you have left/right authoritarians who defend property rights or hide behind a narrow definition of free speech in the first Amendment, over fundamental human rights. Companies like Twitter are now the de facto Town square which have replaced newspaper editorials and other mediums traditionally propagated ideas to a large audience.
A private company could purchase every piece of public land, control all access points to the internet, and effectively been anyone from speaking, and you apparently would be okay with that because "it's not the government".