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. [0] https://www.supremecourt.gov/opinions/16pdf/15-1194_08l1.pdf