The US constitution applies to the US government. For a while, there were questions as to which parts and how much of it applied to state governments. The constitution doesn't really apply to private individuals and organizations, which is why a company can do things like ban neo-nazis from their platforms.
While it’s technically correct that the First Amendment only applies to the US government, it is also true that Americans are (or were) understood to have broad free speech rights that included all facets of life.
Were that not the case, the Hollywood blacklisting of known or suspected Communists would be a nothing-burger and not a cause célèbre.
Nobody at the time called Hollywood blacklisting a First Amendment violation. In fact, the First Amendment offered pretty weak protections for content once deemed pretty subversive, yet considered banal today, until the 1969 Brandenberg Supreme Court decision. For example, in the 1920s you could be criminally prosecuted for openly sympathizing with the Communist party and that was deemed just fine. See Whitney v. California, 274 U.S. 357 (1927).
It shouldn’t be lost on anyone knowledgeable of legal history that every conservative who relies on modern “free speech” principles to insulate themselves from liability for disseminating bullshit to achieve their political gains has a “liberal activist court” to thank for the privilege.
