Not on principle, but in my experience, activity like that usually causes an immediate shitstorm of escalation and greatly heightens the potential for mob violence. Even if that is avoided people are usually wound up, and that results in vandalism on the way out of the immediate area.
If you're a business that's the last thing you want. This is what you're trying to avoid. This isn't the Constitution, so I afford business owners leeway, but my concern is always with opening the door to bad precedent for the other side to exploit this unsound foundation.
What happens if playing to the crowd as a business owner means catering to more racist environments? What happens when you're in small towns that are heavily black or heavily white where the community of the aggrieved isn't as profitable as the community of the aggressor?
This is why it's so essential to understand that merely taking offense to something doesn't inherently assign value to the source of that perceived offense. Just as their is mob justice I have noticed there is a mob victimization mentality. Neither is healthy; the common denominator is the zealous belief of those in the mob that they hold moral authority by virtue of their numbers and cohesion. Of course this isn't true.
This isn't the law. We're speaking to an unwritten cultural morality of civic conduct, here. Specifics rule.