Reason online has published an excellent article by Jacob Sullum explaining how the same libertarian principles that lead to the abolition of slavery and Jim Crow laws also explain Rand Paul’s views on legally preventing private businesses (and consumers for that matter) from choosing who they want to do business with.  These are the principles of self ownership and freedom of association. This passage from Sullum’s article captures the point:

Paul’s position is
based on the same principle that led to the abolition of slavery
and the long struggle for equality that followed it: the principle
of self-ownership.

If we own ourselves, it follows that no one else can own us?the
most obvious way in which slavery violates human rights. It also
follows that we own our labor, which means we decide who benefits
from it and under what terms, and the fruits of our labor, which
means we control access to our property. All these rights were
flagrantly violated not only by slavery but by the racist Jim Crow
regime that succeeded it, which forced businesses to discriminate
against blacks as customers and employees.

The Civil Rights Act of 1964 aimed to eliminate state-imposed
segregation and all other forms of official discrimination against
blacks. While wholeheartedly supporting that goal, which belatedly
implemented the 14th Amendment’s guarantee of equal treatment under
the law, Paul expressed qualms
about the provisions banning private discrimination,
which impinged on the same liberties?freedom of contract, freedom
of association, and property rights?that were routinely disregarded
under Jim Crow.
Paul noted that liberty would not mean much if it did not
include the ability to say and do “abhorrent things.”

But ultimately that is the problem, liberty does not mean anything to progressives. It didn’t in the early 20th Century when they were advocating eugenics and the military draft and it doesn’t in the early 21st Century when they are advocating forced busing and mandatory universal service. “Civil rights” stopped being about freedom and rights several decades ago. This is why the term has largely been abandoned in favor of “diversity,” taking any concern for liberty and rights completely out of the equation–(see Wake County Schools controversy).