Obviously, Rand Paul's opposition to Federal laws that ban racial discrimination in businesses like public restaurants is important on its own merits, but it's also important because it highlights his hard-line libertarian political philosophy.
Paul might not be a white supremacist (even though his views overlap with theirs on some issues), but it's clear that he is totally, absolutely opposed to any Federal legislation or regulation that protects average Americans from acts of exploitation, persecution, or discrimination carried out by private companies.
Enumerating the list of protections Paul opposes would go on forever, so let's take a look at one specific example of Federal legislation that Rand Paul almost certainly opposes: guaranteed overtime pay (also suggested by Jonathan Singer).
An employer who requires or permits an employee to work overtime is generally required to pay the employee premium pay for such overtime work. Employees covered by the Fair Labor Standards Act (FLSA) must receive overtime pay for hours worked in excess of 40 in a workweek of at least one and one-half times their regular rates of pay. The FLSA does not require overtime pay for work on Saturdays, Sundays, holidays, or regular days of rest, unless overtime hours are worked on such days.
The FLSA, with some exceptions, requires bonus payments to be included as part of an employee's regular rate of pay in computing overtime.
I haven't seen Rand Paul specifically say he opposes legislation requiring overtime pay, but I cannot see how he could possibly square the Fair Labor Standards Act with his libertarian political philosophy.
Reporters should definitely continue following up with Paul on his statements regarding Federal civil rights legislation, but they shouldn't limit their exploration of his ideological framework to matters of race. Pressing him on whether he supports the Federal law guaranteeing overtime pay would be a perfect place to start.