(Photo stolen from here
Minipundit lays it out
King was one of the first national figures to stand up and oppose the war in Vietnam. He supported a guaranteed minimum income and took a serious stand against poverty. He self-identified as a democratic socialist. He was constantly persecuted by the FBI, and kept an openly gay ex-Communist socialist (the inimitable Bayard Rustin) as his closest adviser. Any conservative who claims that they support King is either ignorant or lying; same with any "sensible centrist" like Joe Klein or David Broder. King was a figure of the left, and the center and right's attempts to claim him as their own are extremely unseemly.
I wouldn't go so far as to say "Any conservative who claims that they support King is either ignorant or lying". There may be conservatives who support King in some areas of his activism but not others. But I do think that the racisim that fueled and continues to fuel
the conservative movement needs to be highlighted. And for anyone in today's right-wing to claim King as one of their own is patently absurd.