Leaving aside the government for a second, what do people think of the notion that once a business advertises its services to the public at large, it gives up the prerogative to choose whom to serve and not to serve?

Relevant article(and coming back to the govt's role):

Under the Constitution, I have a perfect right to be as racist, sexist and exclusionary as I like in my private life and affairs. But business is fundamentally different. Even if I own my store and work there myself, the fact that I am open to the public puts me in the category of commerce, which Congress may regulate if it affects interstate business and the local government may regulate regardless of its reach.
I'm not ashamed to say that I like the sound of that.