One could not register by party in GA at that time, and there were no Republican primaries there until at least 1968 or later. The Kings backed JFK and LBJ. I don’t think they were for Nixon for governor of CA either. Were they for Eisenhower in 1956; I don’t know. I don’t think people can register by party in GA even now; their party allegiance is determined by which party primary they vote in; the same as in TX.
It is my understanding that MLK Jr. switched to support JFK due to Bobby Kennedy assisting in getting MLK Jr. out of jail.
This documentation is hard to pin down, however. In 2009, Kamau-Imani told Fox News that King’s niece, the Rev. Alveda King, said her uncle was indeed a Republican. But while video of Alveda King’s claim is available on YouTube, Kamau-Imani acknowledged there’s no documentation to back her up.
Thank you for motivating me to do more research. Your answer is correct as it is unclear which party they supported. MLK Jr felt betrayed by both parties and preferred a non- alignment due to the Dixi-Crats.