They can post signs such as "We reserve the right to refuse service." But all the refused customer has to do is claim racism. Often restaurants are targeted and were the example most people used to pass the bill..
It's been my experience that most people who are refused won't go to the police, or do anything to draw attention from the man. I've been in a local gun store and watched someone tell a customer that they wouldn't sell him a thompson, basically because the guy was nuts and shouldn't have a gun even though he would pass the check. They didn't want the potential liability or bad publicity