So tell me Ryler.
A chap gets caught shoplifting from your store. Are you in any obligation to allow him back in again, just because you think it's a public place?
Or a chap comes into your store and is really abusive to you, your staff and other customers, making people leave without buying anything. Are you in any obligation to allow them back inside just because you think it's a public place?
Or a chap comes in, pees all over your floor, do you have to let him back in?
Nope is the answer. It's private property, it's your shop. Up to you who you wish to allow in.