Seriously? Why is there even a question about this?
This is the Pandora's Box that should never be opened. What we end up is a restaurant that doesn't seat gay couples, another that doesn't serve interracial and another as a "whites only"?
You are either open to the public, or you are not. Plain and simple.
Forget the idea that, "Its my business, I can do what I want." Oh yeah? Try doing it without your business license, occupancy license and health inspection? You are not an island unto yourself.
Owning a business is not an excuse for exercising personal bigotry.
I would revoke the business license, occupancy license, liquor license and even the fishing license of any business that refuses service to any potential patron for any reason other than valid cause. Drunk and disorderly - valid; gay - not a valid reason.
There are times when I don't recognize this country as the same one that I left body parts around the world defending. The Cayman Islands is looking pretty good right now.