Why stop at websites? Why shouldn't airlines, hotels, banks, apartments, stores, and private universities ban whoever they like? How about creating a rule banning people who dye their hair blue?
There is - of course - rules around this. Certain qualities like race and sex are protected classes against which you cannot discriminate. To your example - a nightclub very well might discriminate against someone with blue hair.
You should not have rules for behavior outside your community. Second, your rules should be restricted to actions that have an effect on your community.
