Most small businesses can release anyone for any reason, including political views.
It depends on the employment contract.
The 1st Amendment doesn’t apply to private contracts, such as employment.
You are correct. When Pres. Bush was running for his second term, a Bush supporter employed at an East coast ice cream shop belonging to two Ben & Jerry types was fired for being Republican. He went to the EEOC and was told that there are no laws against discrimination on the basis of politics. Of course, that may be different now if Democrats are fired for being obnoxious BO worshipers.