Rand Paul a racist?
No. He was presented with what comes off every time as a classic false dichotomy argument based on what he sees in this instance as an example of the always false premise that the end justifies the means. He is objecting to anti-discrimination laws being applied to individuals and individual businesses because of his stance/belief/view of the Constitutional effects of such laws on individual liberty.
Remember that big-L Libertarianism is ALL based on property rights. From his POV (not necessarily my view - I think the whole question is more complicated than that) civil rights laws are bad because they keep people from using their own private property as they see fit.
I think there are people trying to brand him a racist. I don't think he is, but I do think he is not the brightest bulb in the political building. Of course, he's not going to show as a real libertarian, as the Tea Party has been co-opted by the far right wing of the GOP. I don't think there is justification for the attacks on Paul as a racist. Paul says he is against racism even in private businesses, the issue being one of political and Constitutional philosophy as to anti-discrimination enforcement on and over private property.
It seems to me that Dr. Paul understands that discrimination based on race is unjust but still thinks that the legislative effort to address it does not pass Constitutional muster.
I wonder if we are establishing that it is unacceptable to commit to a Constitutional principle to the point of rejecting legal remedies for injustice; i.e.: anti-discrimination laws that control the activities of individuals and individual businesses.