The entire premise of this thread was to discuss whether or not a public business can violate someone's civil rights by refusing to serve them.
I say no, it cannot.
You are wrong.
Let me put this into a real world context you can easily grasp to indicate how this will work. Jim Bob runs a restaurant, and also happens to hate homosexuals, who, I am sure you will admit, have the same civil rights everyone else does, whatever they might be.
Two drag queens walk into his restaurant on a Sunday afternoon just after he opens to serve the crowd from the local Baptist church where he serves as a deacon. He refuses to seat them for no other reason than that they are gay.
You are now all up in arms because he has violated their "civil right" to eat in his restaurant. You want to join them in a suit in Federal court because of your righteous indignation. You actually run into a competent lawyer who proceeds to advise you that, under the Civil Rights Act, you have no case. The law does not cover discrimination based on sexual orientation.
That proves that businesses have the right to violate your civil rights, if they pick the correct one to violate. I believe it also indicates why the CRA is unconstitutional when it tries to impose regulations on private conduct.