On the one hand the defendants obviously are private companies. Your constitutional right to free speech does not come with soap box attached. Private companies can violate your free speech all they want. It's only the government that cannot do that. Those are well-settled principles.
On the other hand, Google, Twitter and Facebook are so big that banning Trump is effectively the government doing it. The big picture: Data shows that Trump's megaphone has been significantly muzzled in light of bans from Big Tech platforms, particularly Twitter and Facebook. Twitter was long his only megaphone. On the first hand, even the government can muzzle a patron falsely crying Fire! in a crowded theater. Drawing on both private and state action legal principles the social media platforms can impose restrictions on dangerous speech. That they have done, and they have done so on the Fire! principle: only dangerous speech is censored, only dangerous speakers are banned. Do they have the right to ban the speaker permanently, or "indefinitely" as Twitter has done (Facebook has imposed a two-year ban.)? A person yelling Fire! in a crowded theater is punished after-the-fact for the dangerous speech. May the private theater ban him from attending in the future? Clearly, yes. May the government? I don't think so.
Dangerous speech is the easy case. The hard case is may false speech be censored, the speaker prohibited from speaking at all? The answer to that extreme question is no, the liar and disinformationist may not have his vocal chords cut. May the government ban false speech and its speaker? An individual harmed by false speech can sue for libel or slander. Plaintiff would have to prove damage. An arm of the government, a judge or jury, can then penalize the false speaker. In addition the government judge may injoin the false speaker from future libel or slander. Can the government prohibit future false speech when no showing of damage is possible? In general the law has always answered with a breezy marketplace-of-ideas-truth-will-win-out nostrum. In the specific case, I am not sure. Analogizing to the injunction and depending on the specifics of the case, analogizing I think yes, the government could injoin future false speech, but I don't know, and if the government could, man, would the bar be set high. If so, it follows that a private company, even a really big one, may. Even if the state could not injoin such future false speech, a company, even a really big one, could. But what if the company, or as here, a group of companies take action that "significantly muzzles" public, concededly false, speech and its speaker? It seems to me, only that, that the law has recognized a private actor as the equivalent of the state, but I only can opine from the criminal law. You have the absolute right to remain silent from state compulsion to incriminate yourself. That does not prohibit me, a private citizen, from compelling you to speak and incriminate yourself. I can threaten you, I can kick you out of the house, I can ban you to your room, I can fire you from your job if you don't answer my questions. I know of no analogous situation in the criminal law where even a really big company, Walmart, say, is prohibited from doing the same thing that I as an individual may do. We shouldn't get too big for our britches in the case of 46-1. You don't have a right to a "significant" share in the marketplace of ideas. You didn't have the right to go on TV when there were only three networks, effectively a monopolistic cartel. That is infinitely more the case now with the proliferation of media. So "From the desk of 46-1" was a humiliatingly small, failed platform. Like your dick, 46-1, you're not entitled to a big one. His lawsuits will fail.