It took many years of fighting to extend the protections of the First Amendments to the states by incorporation through the 14th Amendment. The fight was mostly a matter of political and religious movements pushing the envelope, various socialists, anarchists, civil rights activists and that religious cult "Jehovah Witnesses". People I think should know how much of our freedom we owe to that particular religious cult. On the Supreme Court itself, we owe a lot to the Justices Black and Douglas. Without these movements and those justices it might still be possible for New York City or New York State to pass laws placing severe restrictions on free speech, assuming that such laws were compatible with the New York State constitution. Thus in Florida there was a law against advocating "miscegenation" and such anti-free speech laws were not "unconstitutional," until activist judges such as Douglas and Black found a way to negate the original understanding of the constitution (or at least the Fourteenth Amendment) and extend the First Amendment to state law making. (To be fair to Justice Black, he believed that he was strictly interpreting the Fourteenth Amendment.... Douglas simply didn't care.)
But even being generous to Thomas, if he does actually mean to say that the Constitution as originally understood does not extend First Amendment protections to actions of the various states, then his program is much more that of a radical reactionary than most people understand. That would mean he believes that New York State can pass a law banning rallies by "subversive" parties and the U.S. constitutions has nothing to say about it.
Jerry