Well, in the first instance, I don't buy the argument that what was achieved through the Civil Rights Act would have been achieved nevertheless. I think that because of the Civil Rights Act and other similar laws the acceptance of racism has declined.
Second, I do not think a libertarian position requires one to oppose prohibitions of racial discrimination by private enterprise and I do not buy the idea that the principled libertarian position is that the CRA was an inappropriate use of government power. As I explained above, the CRA is defensible from a libertarian perspective on several grounds, not least of which is the economic harm attendant to black people being excluded from the marketplace entirely.