You're thinking of the first amendment and other legal institutions. Free speech is a much broader concept than this. Ask yourself what a right to bodily autonomy would be if the government only promised that its officers wouldn't bring harm to you, but any private citizen could: it would be anarchy. The reason there is no legal commentary limiting censorship is because it is difficult to discern in the general case when censorship is itself a speech act. This does not limit you or I from making this distinction as private citizens in the particular case, as here.
> Free speech is a much broader concept than this.
Free speech is exactly and specifically the right to control what expression you and your property are deployed to support. Private censorship isn't merely consistent with it, it is the core of it.
Free speech is, in fact, primarily the right to say what you want, not the right to stop others from saying what they want. I admitted that the latter form is sometimes important, but that imparts no requirement on the rest of us to always agree with it.
>you and your property are deployed to support
In particular: "you and your property" is a much more general concept here then it might normally be. If I lend out my printing press to people then I should be able to say what they print with it. If I sell printing presses at a fair market rate, ie I am satisfied with my side of the transaction, then I shouldn't turn around and impose terms on the use of that press. These two things are qualitatively different, even though they both involve limiting the use of printing presses that were at one point mine.