From the summary of Free Speech and the Regulation of Social Media Content (R45650, Mar. 27,2019):

Some have argued that Congress should step in to regulate social media sites. Government action regulating internet content would constitute state action that may implicate the First Amendment. In particular, social media providers may argue that government regulations impermissibly infringe on the providers’ own constitutional free speech rights. Legal commentators have argued that when social media platforms decide whether and how to post users’ content, these publication decisions are themselves protected under the First Amendment. There are few court decisions evaluating whether a social media site, by virtue of publishing, organizing, or even editing protected speech, is itself exercising free speech rights. Consequently, commentators have largely analyzed the question of whether the First Amendment protects a social media site’s publication decisions by analogy to other types of First Amendment cases.