(* The whole concept of a "protected class" is a slap in the 14th Amendment's face. People are supposed to be protected equally regardless of classifications.)
so a “no shirt no shoes no service” sign should be equally legal as a “no blacks” sign?
Of course not, as the part of my post you snipped shows. A “no blacks” sign is illegal because it's discrimination on the basis of race, not because black people are a protected class. Framing the issue in terms of class membership rather than in terms of decision criteria is a recipe for teaching the public to make bad arguments and acquire bad mental habits.
Maybe an analogy will make this clearer. I presume you've heard of "intellectual property"? It's a catch-all term for copyrights, trademarks and patents. But there's no basis for the concept in common law, in statute law, or in the Constitution. "Intellectual property" is more correctly called by its original name, "propriété intellectuelle".
Treating copyrights, trademarks and patents as different aspects of the same underlying thing is an idea from French law that lawyers have tried to graft into Anglo-American law. But copyrights, trademarks and patents are three different things, each with its own history, legal bases, and limitations. In particular, as the Constitution makes clear, the purpose of copyrights and patents is "To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries." I.e., the government is promising potential authors "Create stuff for us and we'll give you a reward".
That's not a property right. That's what's called a "unilateral contract", the same thing as "Reward, $100 for return of my lost dog".
What's the difference, you may well ask? Huge. If you think of an artist's relation to the cartoon he drew as a property right, then the endlessly repeated lengthening of the terms of copyrights will seem reasonable, because you'll think of a copyright expiration as a transfer of the cartoon -- from owned by him to owned by the public. And you'll think of the "for limited times" bit in the Costitution as an annoying error that Congress needs to work around by achieving the permanent ownership of Mickey Mouse for Disney and his heirs that the "property right" theory implies they're entitled to, using the charade of extending the copyright for a finite period infinitely often instead of making it last forever all at once. But when you think of a copyright as the contract it actually is, it's retroactively lengthening the term of the copyright after the author already accepted the original deal he was offered that's a transfer -- from the public to the author. The government took away the public's right to copy the work after 28 years and gave it to the author for free, same as if they passed an ex-post-facto law saying "Hey, dog owner, we've decided that guy you gave a hundred bucks to when he found your dog is entitled to two hundred."
(Incidentally, all this isn't just me blowing legal smoke. John Paul Stevens made exactly the same point in one of his SCOTUS opinions.)
Anyway, my point is, thinking of antidiscrimination law as a matter of whether someone is in a "protected class" encourages the same mushheadedness as thinking of a copyright as "intellectual property".