The US had the concept of protected classes. As a business, I can refuse to serve fans of the wrong sports team or anyone wearing a blue shirt. I cannot refuse to serve people based on membership in a protected class (race, sexual orientation, etc).

I think that works ok. There is a strong profit motive to serve as many people as possible, and there are consequences for getting reputation as “who knows if they’ll serve you”

So, which I would find it distasteful if a store refused to serve Brexiters, I believe the market would sort that out. I’d only be interested in regulation if the problem actually appears.