Libertarian politicians have to walk like they talk, and they have to possess the intellectual integrity and acuity necessary to answer tough question and explain the answers in ways that bring new understanding. The reason it's different for libertarian politicians is because media will test anyone who is anti-statist, who espouses principled views of politics and who presents as a different kind of politician, especially anyone running as a Republican, and especially if the politician is a threat to the status quo in the political realm.
I don't know if Rand Paul considers himself a libertarian, but he promote many libertarian political positions, and he presents as a man of integrity, a new kind of politician. Recently Paul spoke at Howard University and was criticized for doing so. Ta Nehisi Coates claims that Paul lied about his original opposition to parts of the Civil Rights Act, particularly that a business person ought to be able to refuse business to a black customer. We can quibble over words and defend Paul's recent claim that he has always fully supported the Civil Rights Act, but that would be what politicians like Barack Obama do, not what a libertarian claiming integrity should do. So, I agree with Coates -- I expect more out of Paul.
If Paul is not a libertarian, then he's as close to libertarian as we have in Washington DC, aside, maybe, from Justin Amash, so it still stands that if Paul wants to make a difference, he can't back down. Paul has to understand what his principled stance against the status quo means, and to understand he will be attacked either way he goes. If Paul is going to be attacked, though, he should be attacked for honesty rather than hypocisy and covering up his past words like most of all the other politicians in government.
Paul had it right the first time, and he should've stayed with his position. A businessperson should be allowed to refuse business to anyone the businessperson wants to not do business with. If the businessperson is racist, then he/she will shortly be out of business, and the community will have identified someone they'll want to shun. Afterwards, no other businesses would put up a sign saying "We serve only whites". And even if financial punishment by the community only makes racists pretend they welcome all types of customers, it can also send a societal message -- racism is not accepted -- racism is wrong -- there are consequences for such hatred and biogtry.
We've been trained to think that only government can solve such social problems, and I won't argue if the initial laws were necessary or whether the situation would have evolved naturally so that racists were ostracized and punished for economic discrimination. I also won't argue that government laws were the greatest obstacles to integration for a long time. I will only discuss the present, the 21st century, and say that, now, there's no need for a law preventing discrimination in business, because society can handle those problems, and we should be allowed the moral responsibility to do so, so that such actions of punishing racists are real moral acts, not just laws that have to be obeyed. That's all Paul was saying, and he should have stayed with that position.