Or you only show Jane's posts to her closest friends, to minimize the reach of an idea without directly censoring it. Even if those friends share it you can limit the reach to their closest friends too. If users complain that they're getting their exposure limited base on content, just throw up your hands and say "but it's the algorithms that determine the best content to share to your friends, not us!". I'm pretty convinced that Google and Facebook already actively do this.

You bring up a good point with text generation, which made me think of what can be ascertained by writing style. Certainly gender, nationality or regional location, education level, probably something akin to IQ. I'm not sure whether there exists such a thing as a "writer's fingerprint" but if there is, you wouldn't even be able to write things anonymously even with a fake/stolen/alternate account.