Since most of the people who seem to support the added pressure on media companies by the state to censor "misinformation" seem to be on the hard left, it's time for a civics lesson and a history lesson.
I get that most leftists don't like the First Amendment; but, I do and every true liberal does. Also, most leftists don't like fascism (at least that's what they claim). The only reason why the White House directly pushing for private companies to engage in censorship isn't technically illegal or technically a full on abridgment of the First Amendment is that they're attempting to use these major corporations as a proxy of the state. The ethics of the state trying to compel private actors to censor speech that the state regards to be wrong are no better than actually illegally violating the law. In fact, I think I could argue that it's substantially worse.
Now, historically, this is a real problem for leftists who are keeping their gobs shut about this practice or the leftists who are openly supporting it. The dictionary definitions don't cover this; but, historically, from an economics perspective, the key difference between the communist and fascist dictatorships was that the communists openly owned the means of production while the fascists operated with major companies that were private in name only while being proxies of the state.
To put it simply, the communists owned the newspapers outright and therefore they controlled what people were allowed to see while the fascists allowed the newspapers to have owners that had the deed to the property while threatening the "private" owner if he or she printed anything that the state didn't like.
So, every leftist who is okay with this behavior is okay with precisely the tactic that the fascists used to regulate speech.