He WAS a communist. Now “re-imagined” as a national hero.
But saying he supported communism? Nope. Here's a letter he wrote saying a Christian can't be a communist: https://teachingamericanhistory.org/document/can-a-christian-be-a-communist/. MLKJr was also on good relations with VP Nixon, who's main claim to fame at the time was taking down communist Alger Hiss -- hard to imagine communist supporters having good feelings for Nixon. Basically the only link we have with MLKJr and the Communist Party comes from Kennedy's FBI -- if that's worth anything.
We do have on record MLKSr being a loud supporter of "the party of Lincoln". That changed only after the Dims put MLKJr in jail in Birmingham and MLKSr begged President Kennedy to get his son released. Only after that did MLKSr say he supported Dims (perhaps as part of a shakedown agreement by JFK).
“had delusions that the NAACP was a Communist front”
One of the founders of the NAACP, W.E.B. Du Bois was a communist. He joined the Communist Party in 1927.
https://www.peoplesworld.org/article/from-the-peoples-world-archives-w-e-b-dubois-joins-the-communist-party/