And that these sites not being common carriers, helps.
Wrong.
Social media are common carriers.
They transport posts from different authors and allow them to be viewed by different readers.
{...
A common carrier in common law countries (corresponding to a public carrier in some civil law systems, usually called simply a carrier) is a person or company that transports goods or people for any person or company and is responsible for any possible loss of the goods during transport. A common carrier offers its services to the general public under license or authority provided by a regulatory body, which has usually been granted "ministerial authority" by the legislation that created it. The regulatory body may create, interpret, and enforce its regulations upon the common carrier (subject to judicial review) with independence and finality as long as it acts within the bounds of the enabling legislation.
...}
The point of common carriers is they do not create content, so then are immune to suit over content.
Social media WANT the protection that common carrier status gives them.
Since they do not create the content, they can only be common carriers and nothing else, so they can't be sued over content, and they then also can not censor or discriminate.
Contrast that with something like a newspaper, that even when they publish letter to the editor, they deny some, cut or reduce others, etc.
Newspapers are not common carriers because they create their own content and warn people who send them letters, that they won't necessarily be published.
When US Message Board bans or censors, they most definitely are violating the law, but the problem is the FCC and FTC are way too overwhelmed to do anything about it.
With social media, the stated impressions are the media won't alter, censor, or ban unless very specific legal boundaries are violated so that others are harmed.