can I refuse to serve a customer?

[simon]

If it is not your business, and you are simply someone else's emloyee, then you have no rights or authorisation to refuse a customer service or entry on the basis that you think they are rude. Your employer will be unlikely to want to turn their revenue down simply because of your personal opinion, and even less so because you happen to have had an argument with one of them on Twitter.

If you don't want to serve them, either get another employee to deal with them, or if its that important to you, quit the job.

(Incredibly childish question, by the way).