In interpreting the First Amendment to apply to any other entity than Congress, the Supreme Court is modifying the Constitution; this is outside their authority and, according to Marbury v. Madison, that a law* repugnant to the Constitution is void, and that courts, as well as other departments, are bound by that instrument.
* -- Or judicial act, if you apply the same logic as presented therein.
In the absence of any other support, I might agree.
However, the First Amendment refers to "the freedom of speech", which, like the reference to "the right of the people to keep and bear arms" in the Second Amendment, could be read to refer to an existing right.
I don't agree with the Supreme Court's focus on "due process", but I view the "privileges and immunities" of United States citizens to include an immunity from abridgement of the freedom of speech as well as an immunity from infringement of the right to keep and bear arms.