Alger Hiss never joined it either, and he certainly publicly disavowed Marxism.
Why would anyone believe a word King had to say about his political allegiances and convictions when he was willing to lie to his doctoral committee and steal other peoples' work?
King openly espoused all the talking points which the CPUSA espoused - Soviet-style "full employment laws", unilateral disarmament, etc.
If it walks like a duck and talks like a duck . . .