@TomTomBinks,
I believe you can no serve anyone merely because you feel some sort of ill ease about them.
That ill ease cannot be about gender, race, religion, orientation, age, country of origin, etc. Especially if they hang the sign - "We reserve the right to refuse the right to serve anyone".
I also understand that there might be some who might abuse the sign to discriminate. But at least they have to lie and go through some act of dissemblance to pull it off.
Personally there are merchants in this town I don't patronize because I can't abide with their whiny tea baggery - they even post tea baggy signs with their dribble in their windows.
I think of it as my reserved right to refuse my patronage of anyone.