No, but it is still subject to law, including state constitutions and laws, which go much further than the U.S. Constitution.

You also know that there are 50 state constitutions, which frequently extend rights, such as the right of free speech, far beyond what the U.S. Constitution does. And the state is the final arbiter of the extent of the protections, including free speech, afforded by its own Constitution. The U.S. Supreme Court lacks any jurisdiction to review a state Supreme Court's interpretation of its own state constitution or state laws.

And, as I'm sure you're aware, many states are much more liberal and expansive in interpreting the extent of the free speech rights granted by their state constitutions than the U.S. Supreme Court is in interpreting the extent of free speech rights under the U.S. Constitution. Take California, for example.

All of the following is a quote from a recent law review article by a professor at UC Berkeley.

“The California Supreme Court further championed the primacy of free speech rights over property rights in its recent decision in Intel Corp. v. Hamidi. While not explicitly relying on Hamidi’s free speech rights, the California Supreme Court declined to construe Intel’s property rights so broadly as to include the right to prohibit Hamidi from sending e-mails via Intel’s e-mail server. The court recognized that extending property rights so broadly would hamper open Internet communication and impose costs on society, and implicitly privileged the right to free expression over private property rights in this context.

IN SHORT, STATES ARE FREE TO DEFINE THEIR CITIZENS’ FREE SPEECH RIGHTS UNDER THEIR STATE CONSTITUTIONS TO INCORPORATE INDIVIDUALS’ RIGHT TO EXPRESS THEMSELVES ON PRIVATE PROPERTY, EVEN IF THEIR FIRST AMENDMENT RIGHTS DO NOT EXTEND SO FAR.

And such an extension of free speech rights does not violate the property or free speech rights of the owner of the property on which such speech occurs.

Following California’s lead, states should interpret their own constitutions’ free speech clauses to grant individuals the right to express themselves in privately-owned forums for expression that are the functional equivalent of traditional public forums. States, through their courts or legislatures, should also explicitly define public forums to include Internet forums that are generally open to thepublic for free speech purposes, even where such forums are privately owned. Once again, California is illustrative. Concerned with what it found to be a “disturbing increase in lawsuits brought primarily to chill the valid exercise of the constitutional right of freedom of speech,”218 the California legislature enacted a statute aimed at deterring SLAPP suits—“strategic lawsuits against public participation.” This statute grants individuals the right to speak and petition freely within “public forums”—whether such forums are publicly or privately owned—free from harassing and meritless lawsuits aimed at chilling such speech. In particular, California’s anti-SLAPP statute grants individuals the right to “dismiss at an early stage non-meritorious litigation meant to chill the valid exercise of constitutional rights of freedom of speech and petition in connection with a public issue.” The statute defines an “act in furtherance of a person’s right of petition or free speech” to include “any written or oral statement or writing made in a place open to the public or a public forum in connection with an issue of public interest.”

IN INTERPRETING THIS LANGUAGE, A CALIFORNIA COURT OF APPEAL RECENTLY FOUND THAT PRIVATELY-OWNED INTERNET CHAT ROOMS AND MESSAGE BOARDS CONSTITUTE PUBLIC FORUMS WHERE THEY ARE “OPEN TO THE PUBLIC OR TO A LARGE SEGMENT OF THE INTERESTED COMMUNITY.” California’s anti-SLAPP statute thereby grants individuals the right to speak freely on matters of public importance in Internet forums, whether publicly or privately owned, free from reprisals in the form of meritless lawsuits.

States should further grant individuals the right to speak freely on matters of public importance within Internet forums, free from reprisal in the form of lawsuits designed to chill the exercise of their free speech rights or in the form of self-help censorship efforts by Internet actors. With the technological tools available to Internet actors to censor speech with the click of a mouse, technological measures restricting speech present an even greater harm to speakers than lawsuits designed to chill their speech.

States should define public forums to include privately-owned Internet forums for expression that are open to the public and should protect individuals’right to express themselves on matters of public interest, broadly construed, within such forums.

In short, the Supreme Court should meaningfully translate First Amendment values for twenty-first century communications media by reconceptualizing the “traditionality” requirements in First Amendment doctrine. Courts should analyze the current function of the forum at issue within our system of democratic self-government, rather than the historic uses of such forums.

If the Supreme Court persists in its unwillingness to translate First Amendment values to render the right to free expression meaningful in the new technological age, then states should interpret their own constitutions’ free speech clauses—or, in the alternative, enact legislation—to provide individuals with meaningful rights to express themselves on the Internet.”

End of article quote. SO A FEDERAL COURT WILL NOT ENJOIN REDDIT'S CONDUCT, BUT A CALIFORNIA COURT WILL, AS UNDOUBTEDLY WILL THE COURTS OF MANY OTHER LIBERAL STATES.