He has no case.
Yes he does, precedent was set in the homosexual/ cake shop cases............
If a Black man with a BLM hat was refused service, what do you think the outcry (and legal remedy) would be?
Sure he does! The bar owner has to bake the cake, be run out of business and ordered to pay MAGA-hat 80k!
Neither do homos who sue cake makers, but that hasn't stopped them.
Because a dram shop is licensed by the state and is a public accommodation, I would not be so quick to conclude that there is no case. No case for discrimination perhaps, but that does not necessarily equate to no case.