If you want "free speech" so much, then why aren't you on 4chan and instead post on a highly moderated website like this one? It's the pinnacle of hypocricy.
If HN's moderation and censorship becomes unbearable in some manner, I might indeed set out to find myself a different community to engage with.
But if it's the governmental censorship that makes my online interactions unbearable (say, by requiring that I provide every online platform with my RL identity in the name of keeping children safe), what am I gonna do?
If the majority of people agree with you, you can petition and possibly elect a different government. UK is a democracy.
At its core, the augment for "free speech" is anti-democratic. Someone will control the content online. The real question is who will it be? Democratically elected government or some nutjob like Alex Jones?
And "hypothetical"? Really?
Yes, they are. and the way you're trying to square the circle here is by creating an arbitrary distinction between censorship (which is the evil government doing scary bad things) and 'moderation' (which is private groups doing the same thing, but in like, a good way).
There is no material difference between the two other than the size of the institution doing the censoring. Social norms, by their very definition constrain and civilize people by telling them what not to do or what not to say, either explicitly or implicitly so we don't all behave like a bunch of monkeys in the banana factory.
If there really was such a thing as an 'innate right to voice your ideas', censorship here on HN would be as vile as the government doing it, possible even more so because you at least elect the latter. Clearly it isn't vile though, because without strict censorship discourse here would not be possible.
Norms mean "we don't want to listen to you say that". Censorship means "we don't want anyone to hear you say that".
Say a church installs a porn filter on their network. That's moderation: the members of that community have a set of shared values they are protecting. Members are free to access the content elsewhere or leave the group altogether. By contrast, when they pressure the local library to remove books they don't like, that's censorship.
Conflating the two creates an absurd duality where you either support censorship or you support groups being held hostage to society's vilest elements.
There's no absurd reality here. Everyone supports censorship, people just disagree about where or what to censor. They disagree on their shared norms. The true absurdity is to pretend that there is even one person that is religious in the church but secular in the library, as if the two institutions could be separated because they're buildings in different locations.
Ask any gay person who is a member of a homophobic religious community if they're not being censored or discriminated but merely 'moderated'. Sure they can leave, you can also leave your zipcode and move to one with more liberal libraries. This is the 'twitter is just a private company' line of argument that is farcical on its face.