This is just another stellar example of Ron Paul's astounding misunderstanding of the United States Constitution. Why vote for someone who believes that racial discrimination is constitutional? He's not only legally wrong, he's morally wrong.
Perhaps you can go read the COTUS and tell me where it says a private property owner does not have say over who he allows on his property.
Lots of things are constitutional but not right. I could walk up to you on the street and call you a person who has intercourse with your mother and it would be constitutional. That doesn't make it right though. The COTUS is not about RIGHT and WRONG. It is about setting up rules for a gov't that functions while allowing the maximum amount of freedom to exist in the population. Every rule you add reduces that freedom.
I think you have every right to be a racist. I also believe Al Sharpton has every right to be a racist. If a black man owns a store and doesn't want white people in it he should be allowed to say so.
You make the mistake of many Americans who think they know about our COTUS. You want our legislature to define MORALITY. You want a bunch of Reps and Senators to pass laws saying what someone else would be allowed to do because if they didn't those people might do things you dislike. This is fine and dandy as long as they only pass law you agree with but you give away this power to gov't then complain when it comes back to bite you in the rear with things like an Assault Weapons Ban, Fairness Doctrine, Reverse Discrimination, Abortion on Demand for Minors with no Parental Notification.
Get this straight, the purpose of our gov't was to protect the nation from attack and to establish a framework for interaction within the nation allowing the maximum amount of freedom. If you want to preach morality then go to church. The gov't should be concerned with legislating against only those things which directly harm another. Theft, Murder, Assault, Vandalism, Rape, etc. If you choose to be an ignorant bigot and refuse your services or private property to another due to their race or religion then that should be your business. If enough people feel you are a piece of trash for doing so they can tell you by not doing business with you. Gov't has no place in it though.
The gov't should be blind to all forms of religion, sex and race. That means equal protection under the law. The Jew has his murderer prosecuted just like the Christian and neither is barred from running for office.
You are quick to throw out SCOTUS arguments but it is rare that the gov't EVER says it does not have the right to regulate something. Ask a gov't appointee to decide if the gov't has the right to do something, what answer do you expect to get? It the fault of Americans, both left and right, who were stupid enough to want their guys in Washington to legislate against those other people they disagreed with. Such Americans GAVE the power to legislate morality to gov't but forgot that power doesn't disappear when the other party takes over.
Paul is one to say "tear it down." We should never have given gov't such power in the first place and we need to reclaim it. Giving away freedom to gov't is never a good thing and rarely is it returned.
The bottom line is this nation is full of nosy busybodies who want to legislate what goes on in others homes, bedrooms, doctors offices, and places of business. You would all rather fight about which invasion of privacy you wish gov't to practice rather than simply admit all invasions are wrong and it is up to people to behave civilly, not gov't to make them do so.
Which has been the law for forty years now. But don't let decades of supreme court precedent get in the way of Paul's property-rights excuse when it comes to allowing discrimination based on race. 
Combine that view with Ron Paul's newsletter calling 95% of black people criminals (and complaining that blacks were granted civil rights), along with retaining campaign donations from white supremists, and you get a clear picture of Ron Paul's views about racism and discrimination.