As a businessman myself, I'm not a big fan of turning any business away, and that's important because to turn business away suggests one has pretty strong feelings about his/her reason for refusal of service.

Better to not know, then one does not need to be put in a moral dilemma.  But if a client approaches a merchant and expresses his unrepentant participation in sinful acts (in the belief of the merchant), he should be allowed to deny that person service.