Very different to putting up a sign flat out saying you won't server a certain group of people.
As people have said, technically you CAN refuse to serve anyone, however that is not a license to discriminate as you see fit.
I've actually had an experience on this matter - I have dual nationality and I am mix race (half white). I went down to tenpin's when I was 18-19 and tried to get a pint of beer and play some bowling - my British passport was being renewed at the time so only had my other passport as ID. The guy serving told me that my "ID" wasn't valid as its not a British passport. Told him that I want to speak to the manager - the manager told me the same thing... I kinda wish they just had a sign up saying "British only, we're a bunch of racists" so I didn't have to waste my time stepping foot in the place,
because clearly, if you don't have an ID that says you're British, you won't get served anyways - and they have "the right" to do this in a more hidden fashion.