I am far left, progressive, liberal, but clearly it is totally illegal to refuse to serve someone based on their political affiliation, and it would result in a civil war if allowed on any scale.
The 14th amendment does NOT just prevent state discrimination, but demands states protect all individual rights, one of which is freedom of political expression and affiliation.
Here is part of the 14th amendment:
{...
Section 1. All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside. No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.
...}
When it says, "nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws", that means states are required to pass laws to protect all individual rights. That does not just mean states have to outlaw slavery, but that state have to outlaw political discrimination as well, since obviously political speech and association is an important individual right.