Freedom of Speech Versus Property Rights
Civil censorship on a private platform does not violate freedom of speech. Rather, it is unwanted speech on a private platform which violates the essential freedom of property rights.
Free speech entails only a promise by the government, that they will not silence speech that does not impose a clear and present danger, unless silencing such speech is an unavoidable and incidental part of the process of prosecuting an unrelated crime committed by the speaker.
For example, suppose a burglar breaks into someone's house, steals everything, goes home, puts it away, goes back out to a public park, and gives a riveting and inoffensive lecture on various species of birds. It would be unreasonable to expect the government to refrain from arresting this person just because they're in the middle of giving a talk.
So, to reiterate, two relevant points here:
Free speech is a promise that the government will not silence you. It does not mean your fellow citizens cannot silence you. The constitution protects private citizens by restricting the government. It does not restrict private citizens. For that, we have other laws.
Free speech does not protect you against the government displacing you while you are speaking, if they must do so because you have committed a crime.
Finally, I ask you to consider that trespassing is a crime.
So, to draw an inference from these three premises: It is not a violation of your freedom of speech for your fellow private citizen to demand that the government remove you from their private property because they dislike what you are saying there.
To again break down the reasoning here:
Once the owner of the property you're using as a platform doesn't like what you're saying, it follows they might not want you there anymore.
Once they don't want you there anymore, then should you choose to remain there, you are trespassing.
Once you are trespassing, you are committing a crime.
Once you are committing a crime, the government is within their rights to displace you, even if you are incidentally silenced in the process.
Therefore, transitively: if you're using a private platform, and its owner disagrees with what you say, then you do not have the right to say it there. You have the right to say it, but you do not have the right to say it there, because, strictly speaking, you do not have the right to be there.
This rhetorical demonstration that censorship on private platforms is morally acceptable refutes the concerns of right-wingers who cry out about their freedom of speech when, say for example, they're banned from social media for being nazis.
(Never mind that nazi-adjacent speech is already excepted from constitutional protection anyway, because incitement falls into the category of clear and present danger. That is true, and more important. But it is also more debatable. Nazis would like us to believe incitement is not a clear and present danger. But they cannot possibly have anyone believe property owners are not entitled to the castle doctrine. Not when they themselves so often rely on it.)
Nevertheless, there are some right-wingers so extreme that they would declare it "censorship" when fellow individual people simply refuse to listen to their hate speech. To them I have this to say:
How do we define a platform? How large must a platform be? Is a single grain of sand a beach?
I assert that even one person's attention can be a platform.
Who owns one person's attention? Trivially: that person.
Therefore: if you say something to someone that they don't want to hear, then you are trespassing upon the private platform that is their attention, and therefore they, as the owner of that platform, are within their rights to remove you from it, even if this incidentally silences you.
Freedom of speech entitles you only to speak. It does not entitle you to be heard. If you're going to spout vile shit, people don't have to listen. What about their freedom? Haven't you ever heard of a "captive audience?"