As I understand him, private companies should decide for themselves who they serve and if we think they are behaving immorally, convince our circle not to give them business. It's not the government's job to say who they can and cannot serve.

https://www.washingtonpost.com/blogs/fact-checker/post/rand-...

    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.

    INTERVIEWER: But?

    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. 

    INTERVIEWER: But under your philosophy, it would be okay for Dr. King not to be served at the counter at Woolworth’s?

    PAUL: I would not go to that Woolworths, and I would stand up in my community and say that it is abhorrent, um, but, the hard part — and this is the hard part about believing in freedom — is, if you believe in the First Amendment, for example — you have to, for example, most good defenders of the First Amendment will believe in abhorrent groups standing up and saying awful things and uh, we're here at the bastion of newspaperdom, I'm sure you believe in the First Amendment so you understand that people can say bad things.It’s the same way with other behaviors. In a free society, we will tolerate boorish people, who have abhorrent behavior, but if we're civilized people, we publicly criticize that, and don't belong to those groups, or don't associate with those people.