Ron Paul is a champion of Civil Rights and the Constitution, the two go hand and hand, these are the foundations of classic liberalism and humanitarianism....Librtarianism comes from classic liberalism... It would be convenient for libertarians if the civil rights movement were indeed broadly libertarian but its really not technically although it is philosophically in many ways. Also, Like any good person, libertarians can identify with the civil rights movement's pleas for meritocracy and against blind hatred.
Unlike libertarianism, the civil rights movement rarely distinguished between state and private discrimination. King also supported many left wing ideas such as banning prayer in school and entitlement programs, he allegedly surrounded himself with "Communist". One could argue that MLK was very left wing by todays standards in comparrison to Ron Paul, this is a very easy argument to make.
But I will make some points here on specific issues how we can see MLK as similar to Ron Paul, Libertarianism, and also Conservatism. I see MLK as a sort of socialist libertarian in the classic sense but it can be argued that MLK was a libertarian for a multitude of reasons. Again is really hard to compare the two based on technical reasons because there is essentially none but this is what there is from a from a technical perspective and not philosophic
*They were/are both anti-war
*Both have/had PHDs
*Both are/were Average men who took on the state and were successful. (Philosophically MLK did not take on the state but he technically he did)
Really thats it for Technical View...but philosophically they are alike in many ways...