Sounds like censorship to me, just a socially acceptable form of it. The "only governments are capable of censorship because my understanding of the idea of freedom of speech deliberately stops at the First Amendment" meme needs to die.
No, it damn well is not.
Freedom of speech is the principle, the first amendment is the law. The law protects a principle our society has deemed important. The principle exists with or without a government.
Which literally nobody here suggested that they should be obligated to do so. What's your point?
However, this does not mean that a private company is obligated to give you a free platform to disseminate your speech. You can go make yourself a sign and stand on a street corner if you want, but no one has an obligation to listen to you, or to help you spread your speech.
This is why the distinction about government censorship is so important. People like you seem to think that private entities have an obligation to host other peoples' speech. If some neo-Nazis knocked on your door and asked to post a bunch of their signs on your lawn, would you agree to it? It's only a problem when the government censors because there's only one government, and they have enforcers who can use deadly force. If a private party censors you by refusing to help air your views, you can go somewhere else, like a street corner, and you don't have to worry about going to jail or being shot.
I would add that it's also because the government can censor people when it otherwise wouldn't be involved - a person hosting a blog with a third party, for example. Ordinarily, only that third party gets to decide whether or not to provide a platform for your data.
Going a step further, there's nothing inherently wrong with censorship.
So long as they're censoring the things you want them to censor. Of course, everybody would like something different to be censored, which is why it's better to err on the side of "no censorship". There's a reason librarians tend to fight against any form of censorship.
> Censorship: the system or practice of censoring books, movies, letters, etc.
> Censoring: to examine in order to suppress or delete anything considered objectionable
On a side note though, if it's fictional stories and art involving under age people, that's actually legal (kinda/sorta/not tested often in court) in the US and Japan but not in most of Europe (including France).
For example: drawing of Bart fucking Lisa Simpson. Legal in the US (and if you argue it right, possibly not even a trademark violation under parody/satire -- depends on the judge really). In the UK, that exact drawing sent a man to prison and put him on the sex offender registry.