And the 14th Amendment incorporates that onto state and local governments.
As decided in the Slaughterhouse Cases in 1873, there was no overarching "incorporation clause" in the 14th Amendment. The original intent of the 14th Amendment, as confirmed by the Slaughterhouse Cases, gave the feds ONE SPECIFIC power over the states: to forbid state laws forcing segregation of former slaves, blacks. THAT'S IT. As the Slaughterhouse opinion warned, anything more is not only not the original intent of the post-civil war amendment, but would give the feds carte blanche, destroying the Constitution and its limitations on the federal government.
Such has been the case since the 20th Century SCOTUS has overturned the Slaughterhouse precedent and twisted the 14th Amendment to allow the federal government to run amok with no Constitution-based justification or reasoning to do so.
Proper application of the Constitution requires finding the original intent of what was written. The 14th Amendment is especially a case in point because it was unfortunately so badly and hastily written. The 14th Amendment is only meant to allow the feds to prohibit state (not individual or business) segregation requirements ("equal protection"). You need to do a non-Progressive-tailored study of the post-civil-war reconstruction period when the 14th Amendment was passed and the opinion of Justice Miller in the Slaughterhouse Cases.