You may not believe that is what is happening, but to those people who are subject to refusal of service from a *public* shop, it is just the same.
At one point I was all for pushing against idiots like these kinds of shop keepers. You want to deal with the public, you have to accept ALL public, regardless of your "beliefs".
But now despite the discrimination, I'm all for saying "Fuck them" and go find someone else to take your business, and just make sure everyone in the public realizes the kind of shitbags these people are.