In the American context, these are universal appeals. King pleaded for the fulfillment of America's classically liberal revolution. At the core of that revolution was the concept of negative liberty -- being free from government-imposed oppression. That is why the Bill of Rights is framed in the negative or designed to restrict the power of government. "The Congress shall make no law" that abridges freedom of speech, assembly, etc.
This arrangement has never fully satisfied the left. The founding philosopher of American progressivism, John Dewey, argued for positive rights: We have the right to material things -- homes, jobs, education, health care, etc. Herbert Croly, the author of the progressive bible "The Promise of American Life," argued that the founding was unfinished and only by turning America into a European-style cradle-to-grave social democracy could our "promise" be fulfilled. Franklin D. Roosevelt tried to in effect replace the Bill of Rights with a new "economic bill of rights" along these lines. That was the intellectual tradition of Randolph and, to a significant degree, Barack Obama.
The problem is that, in America at least, appeals to social planning and guaranteed economic rights are not universal. They are, deservedly, controversial and contestable. They are all the more so when decoupled from the idea of colorblindness.
Which brings us to another compelling historical surprise. Conservatives, who were too often on the wrong side of civil rights in 1963, are champions of race neutrality, while King's self-appointed heirs are more inclined to champion the ideas that never spoke to the hearts of all Americans, or to mint new causes they assure us King would have cared deeply about had he lived. That's their prerogative, but they shouldn't be surprised when such efforts fail to capture the hearts and minds of all Americans.