Rand Paul, Tea Party favorite who won the Republican Senate primary in Kentucky, disagrees with the 1964 Civil Rights Act's effect on private business. Paul explained his views in an interview with the editorial board of the Louisville Courier Journal:
Interviewer: Would you have voted for the Civil Rights Act of 1964?
Paul: I like the Civil Rights Act in the sense that it ended discrimination in all public domains, and I’m all in favor of that.
Paul: You had to ask me the “but.” I don’t like the idea of telling private business owners—I abhor racism. I think it’s a bad business decision to exclude anybody from your restaurant—but, at the same time, I do believe in private ownership. But I absolutely think there should be no discrimination in anything that gets any public funding, and that’s most of what I think the Civil Rights Act was about in my mind. (h/t Think Progress)
Paul upholds the "freedom" of businesses to bar fellow citizens based on skin color. He doesn't uphold the freedom of all citizens to patronize whatever business they want without fear of discrimination. The government enforced federal law to prevent such mistreatment. Regardless of the fact that he does not likes the idea of discrimination, Paul upholds it. The Louisville Courier-Journal put it well in an editorial:
The trouble with Dr. Paul is that despite his independent thinking, much of what he stands for is repulsive to people in the mainstream. For instance, he holds an unacceptable view of civil rights, saying that while the federal government can enforce integration of government jobs and facilities, private business people should be able to decide whether they want to serve black people, or gays, or any other minority group.