The slippery slope could go farther than a ban from the premise for retail theft. People are being barred from banking in England based on political speech. Don't grocery stores have the right to choose who they do business with? What if they don't want transphobes, Brexiteers, or people of Russian descent shopping there?
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.
"The market" will consolidate grocery stores until only 3-4 nationwide chains remain, whose policies and prices will be suspiciously similar. Almost every market is moving in that direction, and some have already arrived.