So I want to expand on this argument that there is a difference between consensual relations between individuals and consensual relations between individuals and businesses. The thing that Rand Paul gets wrong is that business transactions don’t happen in a vacuum, they happen in a market. Markets (at least legal ones) have the feature that they feature a varied and rich legal architecture binding a business to the larger communities like the cities and states where they have business licenses. In some senses this is a very democratic notion: markets should be accessible to anyone regardless of race because it is only through the regulatory functions of representative governments that they are able to exist in the first place.
In other words, if we have to give everyone suffrage regardless of race, we have to ban racist business practices.
Think of the analogy to building codes. Businesses operate under the very real parameters that they have to conduct business in buildings that are physically safe. If these buildings were not physically safe, and were for instance in a negligent state that inappropriately risked catching on fire, then there are serious obvious negative externalities that exist. If one building is on fire, other nearby buildings are at risk, and there is damage to property and life that must be evaluated. Hence, we have building codes and fire codes (regulations) to mitigate these risks so that one business can co-exist with others in geographic space.
Regulation against racism is much the same. Has anyone ever proposed to Rand Paul that in a world where he refused to regulate racism, racist businesses risk being focal points for violence and riots? The public safety considerations are substantial and presumably justify quite a lot of government intervention (anyone remember the Rodney King riots?) You could come up with a variety of empirically relevant scenarios here.
I understand that part of Paul’s argument is that federal regulation is not necessarily good. That is conceded. But the part of his argument that says government shouldn’t intrude on private conduct does not extend to business conduct and I think it is important that people understand that.
Ducks and Economics 
Hadn’t thought of this angle on the Rand Paul story… well done.
We’ve been trying to talk through this from a couple of different angles here http://bit.ly/aNQwLL
I was actually surprised to see how many quibbles a dyed-in-the-wool Libertarian had with Mr. Paul on a lot of pretty important issues. Goes to show the benefit of people stopping their yelling long enough to hear what the other side has to say.