MLK was neither a Republican nor a Democrat. He voted for JFK and LBJ. He did not want anyone to vote for Goldwater. So???
MLK was an interesting guy. He hinted he was a Republican because he hated the segregationist southern Democrats. I saw that one go both ways in the history books. He distrusted Kennedy at first but warmed to him after JFK backed his and Abernathy’s safety while in jail.
And he may have voted for him, but he became a huge pain in the neck for Johnson, certainly no longer a fan by the time of his death. MLK was training his gunsites on the Vietnam War.