The guy with no shirt and no shoes does not have an anti trust lawsuit because McDonalds, Burger King, and Wendy's all decided to prohibit his entry into their restaurants.
Sometimes the customer is the reason they all make the same decision.
That's if it is equally applied to everyone. Examples, similar to yours, are used as basis of racial discrimination lawsuits when the evidence shows that it is selectively applied to a group of people.
Discrimination is perfectly legal in the US. It is only illegal if you discriminate against someone within a protected class on the basis of them being a member of that protected class. Political affiliation is not a protected class.
Sometimes the customer is the reason they all make the same decision.