MLK, like JFK, RFK, and LBJ*, came from an era better than this one; it's easy for me to sympathize with him and his marchers, dressed like me and appealing to noble principles, defending the rights of people historically oppressed. A heady mix of Christian values of charity and justice and space-age idealism, liberalism's belief in man's and society's perfectibility. (The Great Society!) But all principled American conservatives in the golden era opposed the civil-rights movement, I think simply because constitutionally it didn't have a leg to stand on. The dilemma: blacks' rights vs. some whites asserting THEIR right to freedom of association. You may well be mean-spirited but that's your constitutional right: the government can't make you associate with someone you don't want to be with, as long as the other person's rights are protected too. Separate but equal was an attempt to solve this legal conundrum. In a free country there is no such thing as thoughtcrime. Basing the law on feelings, however well meant, replacing logic or precedent, is bad. So, if not the status quo nor the movement, what? It's too bad the silent majority, Middle America's pushback then, seemed not to come up with an answer. My guess: the answer is a color-blind government; neither racial bans nor special treatment. Let the outcomes happen as they will. White Americans have no agenda against black ones.
Related: the "me too" Republican Party desperately looking for black candidates/spokesmen, because establishment conservatives have lost their nerve, buying into the ruling left's narrative.
*The '60s: the Initials Decade in American politics. If only Barry Goldwater had catchy initials. (His campaign pin is on my desk.)