The scenario you presented is basically so hypothetical as to border on absurd, and you keep getting more absurd by then asking if it's ok for a restaurant to exclude Republicans or Democrats, etc...
In the first scenario, KKK people hate Blacks, correct? Why would they, then, go to a restaurant owned by a Black man, who could spit in his food if he wanted to? The Black man just happens to know that the guy is KKK, most likely because he lives in a small town, eh? Anyways, I voted yes, he can ask him to leave.
And, why in the world would a restaurant, in the business of making money, want to turn away half their customers based on political affiliation? The profit margin in the restaurant business is slim. If the restaurant wants to go out of business, then it can start arbitrarily turning people away and pissing off all their friends and neighbors.
There was a doctor somewhere back east who put a sign on his office suggesting Democrats who support National Healthcare to take their business elsewhere, it made the news but I think he had the right to post the sign, so yes, if the restaurant wants to tell people to shove it, I guess they have a right to most likely go out of business.