Well, I disagree with you.
While i believe all publicly owned entities should, private businesses are just that, private.
Don't get me wrong, if I had a business in AZ, I'd welcome everyone through my doors, as long as they were good peeps, but that is my decision and i don't feel government should have the authority to take away my rights, in favor of others.
If a latino or white dood went strolling into an African American barber shop, and the owners said he doesn't want to give them a hair cut, I'd stick up for that barber shop owner's rights.
Nothing bigoted about it, just principles.