This whole "free speech" issue is so clouded by liberal assumptions...
Without political power, curtailing public expression is ineffective. Here in the freest country in the world, the Constitution proclaims that Congress will not interfere with the exercise of free speech (among other things), and because of our public indoctrination (oops -- of course I mean education), Americans have some strange ideas about what that means. For example, many believe that if some publisher ignores a story/contribution, then that's censorship. This is absurd; there is no implied duty or responsibility of a publisher to print/broadcast any particular opinion. Ignoring or refusing to publish/broadcast somebody's opinion is not the same thing as suppressing or censoring it. Those actions are almost always the purview of government agencies (especially those relating to security and law enforcement). People without access to political power (the power to repress) cannot really be censors.
The American idea of Free Speech is really a legislative issue. The justification for curtailing it (the "clear and present danger" test) arose first against a Socialist (Schenck) and then anarchists (Abrams, et al), all of whom were engaged in anti-war agitation. When the Wobblies started their free speech fights, it was to showcase the hypocrisy of US law enforcement and the judiciary rather than some principled stance in favor of any opinion being expressed publicly.
Mostly when people complain about censorship and Free Speech, they are adhering to some liberal ideal about the free circulation of opinions in the Marketplace of Ideas. This is absurd, and results in the extension of freedom to the enemies of freedom -- like when the ACLU defends nazis on the grounds of some alleged right to freedom of speech, invoking Voltaire's "I do not agree with what you have to say, but I'll defend to the death your right to say it." The very fact that the entire discourse occurs within the realm of rights should make anarchists skeptical.
Free Speech is an American shibboleth, and has almost nothing to do with anarchism.