There seem to be a lot of different threads of argument here and lots of the discussion seems to meander between them.
The way I see it:
- The "town square" concept (and whether individual social media apps/websites constitute what is historically called that in the legal realm). Can a person say something which should get them banned from a town square? What if multiple town squares coordinate their actions against a single user/content?
- Private party "censorship". Is what social media companies do "censoring"?
- The role of 1st Amendment in "protecting speech" of private individuals against private companies (which historically is not covered by the 1st Amendment, but is covered by the principle of Free Speech)
- The role of 1st Amendment in "protecting speech" of private companies against the president (which might be covered under the 1st Amendment, depending on other factors)
- Whether the 1st Amendment protects from threats from government officials, as opposed to actions of officials
- Private sector companies using their own moderation rules+workforce (including vague rule definitions and no ability to get a judgement about where "the line" is)
- Brigades of political activists using the moderation systems against their adversaries
- Whether the political tendencies of employees at the relevant social media companies have any significant bias for/against specific users/content
- Whether a private sector company is allowed to curate content on its property (and the sub-arguments which revolve around ToS/EULA/contracts)
- Legal responsibilities+liability of social media "platforms" under "Section 230" (and some people misunderstand this industry to be under Common Carrier laws, which regulates more commoditized telco systems)
- Second-order effects of account bans, including loss of access and content under shared accounts (eg. getting banned from your Facebook account also leaves you locked out of any account you connected with Facebook Connect / OAuth)