Rand Paul, Meet Max Weber
Let’s start with Max Weber’s definition of the state, which libertarians often embrace: The state is a monopoly on the legitimate use of violence.
Legitimacy can be granted in a variety of ways, both formal — as with a written public law — and informal — as with the universal understanding that anyone who crosses the color line is a potential target, whether white or black. Violence is further legitimized when it’s a foregone conclusion that the perpetrators will go unpunished. Which of course it was.
By this understanding, racial violence in the South was clearly and obviously legitimized through the state. And if I’m right on that, then racial violence was an appropriate target for legislative reform.
Yes, this legislation interfered with how some businesses preferred to operate, and yes, in a perfect world it would never have been necessary. But it was necessary, to break a system of organized violence that effectively prohibited even willing, consensual integrationists from dealing squarely with the members of other races. Other methods had even been tried in the past, and they had all failed.
So in the longer term, this interference with willingly racist business owners maximized liberty for a much larger class of people who had been deprived of it, including both blacks and whites. It broke a form of concerted (and indeed, compelled) action, one underpinned by state-legitimized violence.
The 1964 Civil Rights Act was a complex set of tradeoffs, but ultimately a wise one. Even by libertarian standards.