> It might even be a proxy for some illegal discrimination prohibited by law <
Yes, but such a thing should not be stretched too far. Otherwise, property rights would disappear. The federal government has laws against discrimination. But anything not covered by those laws should be fair game. For example, many restaurants have a “no shoes, no service” policy. They are discriminating against people who prefer to go barefoot.
That discrimination is perfectly legal. And it should be, if property rights are to mean anything.
“No shoes, no service” is from the municipal Health Department. No Dogs Allowed is usually the same.