The recent Section 230 executive order[1] would be relevant here. Normally social networks have immunity from prosecution if they publish a defamatory or libelous statement (this is the so-called "magazine stand" model). But if the executive order is legal then selectively censoring (or "moderating") what your users post means that immunity no longer applies and you can be sued for any statement that you allowed a user to publish on your network.

This isn't directly related to First Amendment freedom of speech rights, the issue is one of liability (but the purpose of the liability is -- allegedly -- to force platforms to uphold the principle of freedom of speech).

[1]: https://www.whitehouse.gov/presidential-actions/executive-or...