Would-be censors love to claim that only governments censor, but that claim can only be made by people who reject dictionaries. As the ACLU notes, "Censorship, the suppression of words, images, or ideas that are "offensive," happens whenever some people succeed in imposing their personal political or moral values on others. Censorship can be carried out by the government as well as private pressure groups."
Silencing opponents is not a left or right tactic, as anyone who remembers Joe McCarthy and Chairman Mao ought to know. It's just a tactic loved by people who think their cause justifies ethical shortcuts.
Here's a lovely paen to the free press: "The free press is the ubiquitous vigilant eye of a people's soul, the embodiment of a people's faith in itself, the eloquent link that connects the individual with the state and the world, the embodied culture that transforms material struggles into intellectual struggles and idealises their crude material form. It is a people's frank confession to itself, and the redeeming power of confession is well known. It is the spiritual mirror in which a people can see itself, and self-examination is the first condition of wisdom. It is the spirit of the state, which can be delivered into every cottage, cheaper than coal gas. It is all-sided, ubiquitous, omniscient. It is the ideal world which always wells up out of the real world and flows back into it with ever greater spiritual riches and renews its soul."
The author is Karl Marx. Identitarian leftists, with their love of controlling other people's speech, are an odd mixture of middle-class moralists and old-fashioned authoritarians. They have nothing to do with people who respect Marx's thought.
ETA from A.C.L.U. Slams John Bassett Cancellation of Dr Finkelstein Talk at Clark University:
...the cancellation of his speech violates the basic principles of freedom of speech and academic freedom which are so fundamental to an institute of higher learning. The existence of an opportunity to speak at another time or in another location does not remedy the wrong of censorship.