The challenge is that, at least in the US, these platform have sought to secure themselves the "public space" status through Section 230 immunity under an economic difficulty argument. So, yes they are private entities, but they have been claiming to be public spaces who shouldn't be burdened with this.
> The challenge is that, at least in the US, these platform have sought to secure themselves the "public space" status through Section 230 immunity under an economic difficulty argument.
It makes perfect sense that they would be free to refuse to publish content they object to, even with 230 immunity, and the courts agree.[0]
> Do I lose Section 230 immunity if I edit the content?
Courts have held that Section 230 prevents you from being held liable even if you exercise the usual prerogative of publishers to edit the material you publish. You may also delete entire posts. However, you may still be held responsible for information you provide in commentary or through editing.