Case law would disagree. Here's a case where the Supreme court ruled that Facebook banning someone was a violation of their first amendment rights. [0] Salient quote: "Foreclosing access to social media altogether thus prevents users from engaging in the legitimate exercise of First Amendment rights"
Edit: as pointed out, this ruling doesn't actually disagree with what the previous comment said. It does seem similar enough to me to be relevant though so leaving it up.
That is a restriction on lawmakers, not a restriction on Facebook. The law was found unconstitutional. Facebook didn't have to do anything here. As far as I can tell, he was never blocked or banned on Facebook's platform to begin with.
Ahh, right you are. That is an important distinction. Still, it seems a little odd to me that it results in the same thing and is treated differently. What if a government asked Facebook to ban someone and they complied, is that Facebook doing it or the government.
Government is doing it. If Facebook is doing it at the direction of a government entity and would otherwise not do it (and this is where I would expect case law to get into the contextual details of implicit/explicit direction etc) then government is acting in violation of the first amendment.
It doesn't result in the same thing. If Facebook bans someone, they can't log in. If the state bans someone, they can be fined or jailed. And in this particular case, he was banned from all social media and a bunch of other websites.
I Am A Former Lawyer: cursory reading of that judgment shows it as a case of the State of North Carolina passing a law asking it illegal for someone to use a commercial social network service. Presumably Facebook are banning a user in response to a state’s law enforcement request under State law. The Suorene Court is most likely ruling that the state law was in violation of the first amendment.
Edit: as pointed out, this ruling doesn't actually disagree with what the previous comment said. It does seem similar enough to me to be relevant though so leaving it up.
[0] https://www.supremecourt.gov/opinions/16pdf/15-1194_08l1.pdf