"...censorship is a concept that pertains *only* to governmental action." [updated]

"Freedom of speech means freedom from interference, suppression or punitive action by the government -- and nothing else. It does not mean the right to demand the financial support or the material means to express your views at the expense of other men who may not wish to support you. Freedom of speech includes the freedom not to agree, not to listen and not to support one's own antagonists. A 'right' does not include the material implementation of that right by other men; it includes only the freedom to earn that implementation by one's own effort. Private citizens cannot use physical force or coercion; they cannot censor or suppress anyone's views or publications. Only the government can do so. And censorship is a concept that pertains only to governmental action."

~ Ayn Rand, from her column 'The Fascist New Frontier,' collected in The Ayn Rand Column

"For years, the collectivists have been propagating the notion that a private individual’s refusal to finance an opponent is a violation of the opponent’s right of free speech and an act of “censorship.”
    "It is 'censorship,' they claim, if a newspaper refuses to employ or publish writers whose ideas are diametrically opposed to its policy.
    "It is 'censorship,” they claim, if businessmen refuse to advertise in a magazine that denounces, insults and smears them . . . .
    "And then there is Newton N. Minow [then chairman of the Federal Communications Commission] who declares: 'There is censorship by ratings, by advertisers, by networks, by affiliates which reject programming offered to their areas.' It is the same Mr. Minow who threatens to revoke the license of any station that does not comply with his views on programming—and who claims that that is not censorship....
    "[This collectivist notion] means that the ability to provide the material tools for the expression of ideas deprives a man of the right to hold any ideas. It means that a publisher has to publish books he considers worthless, false or evil—that a TV sponsor has to finance commentators who choose to affront his convictions—that the owner of a newspaper must turn his editorial pages over to any young hooligan who clamors for the enslavement of the press. It means that one group of men acquires the 'right' to unlimited license—while another group is reduced to helpless irresponsibility."

~ Ayn Rand, from her article 'Man's Rights,' collected in The Virtue of Selfishness

Hat tip Gus Van Horn, who observes that the misunderstanding she identifies persists today; that the complaints made by "collectivists" in Rand's day "are basically identical to the ones conservatives like to make about various social media outlets today" -- and that while Elon Musk's heart appears to be "in the right place" on free speech, he still seems to labour under the illusion that "support for free speech merely means support for whatever the government happens to allow." Which is simply not the case.

To be clear [says Van Horn], while I often disagreed with the way Twitter moderated its platform, I appreciated then (and do now) that it is, ultimately, its owner's property to do with as he pleases. 

    But that doesn't make it any less disturbing to see Elon Musk riding in like the white knight he intends to be -- but spouting the same nonsense about (what the left has caused everybody to regard as) "censorship," thereby helping pave the way for the government to come in and impose the real thing.

 That said, argues Truth on the Market, while acknowledging that "Musk’s idea that Twitter should be subject to the First Amendment is simply incoherent" -- and, worse, by further confusing folk about who can censor whom, perhaps pave the way for real censorship to grow legs (disinformation commissars, anyone?)-- "his vision for Twitter to have less politically biased content moderation could work."

There has been much commentary on what Musk intends to do, and whether it is a realistic way to maximise the platform’s value. As a multi-sided platform, Twitter’s revenue is driven by advertisers, who want to reach a mass audience. This means Twitter, much like other social-media platforms, must consider the costs and benefits of speech to its users, and strike a balance that maximises the value of the platform. The history of social-media content moderation suggests that these platforms have found that rules against harassment, abuse, spam, bots, pornography, and certain hate speech and misinformation are necessary.
    For rules pertaining to harassment and abuse, in particular, it is easy to understand how they are necessary to prevent losing users. There seems to be a wide societal consensus that such speech is intolerable. Similarly, spam, bots, and pornographic content, even if legal speech, are largely not what social media users want to see.
    But for hate speech and misinformation, however much one agrees in the abstract about their undesirableness, there is significant debate on the margins about what is acceptable or unacceptable discourse, just as there is over what is true or false when it comes to touchpoint social and political issues. It is one thing to ban Nazis due to hate speech; it is arguably quite another to remove a prominent feminist author due to “misgendering” people. It is also one thing to say crazy conspiracy theories like QAnon should be moderated, but quite another to fact-check good-faith questioning of the efficacy of masks or vaccines. It is likely in these areas that Musk will offer an alternative to what is largely seen as biased content moderation from Big Tech companies.
    Musk appears to be making a bet that the market for speech governance is currently not well-served by the major competitors in the social-media space. If Twitter could thread the needle by offering a more politically neutral moderation policy that still manages to keep off the site enough of the types of content that repel users, then it could conceivably succeed and even influence the moderation policies of other social-media companies.
Let the Market Decide
    The crux of the issue is this: Conservatives who have backed antitrust and regulatory action against Big Tech because of political bias concerns should be willing to back off and allow the market to work. And liberals who have defended the right of private companies to make rules for their platforms should continue to defend that principle. Let the market decide.