Anything you want to censor has at least 5 stages:

Creator, first share (direct), second order sharing (public-ish website), third order sharing (indexed resharing), and finally the consumer wanting it presented.

In the way there are things we clearly want to censor for being awful, there are things we must never allow to be censored. Eg knowledge of a genocide.

But the solution kind of rights itself. To censor something you need as many actors as possible in that enormous graph of sharing nodes to clearly want to censor that thing we all agree we clearly want to censor. I.e. a public library doesn't censorship child porn because they are required to.

> Isnt taking down illegal content censorship?

So yes this is censorship, but 'illegal' content is too vague.

We want to know about the censorship beyond the natural baseline.

Censorship, usually, means the extraordinary request for powers to control the web of communications - in the context of what and why.