So you don’t really have any proof.
We know that his dad was a republican, until he switched parties, but I’m not aware of proof of MLK being republican, nor that he was pro-GOP in the 1964 election, or in the 1968 primaries.
“Late in 1967, building upon anti-war sentiment, Senator Eugene McCarthy of Minnesota entered the race, making his challenge to the president no mystery, with heavy criticism of his Vietnam War policies. Even before McCarthy’s entrance, Johnson grew concerned about a challenge. He confided to Democratic Congressional leaders that an opponent could pull Martin Luther King, Jr. and Dr. Benjamin Spock into their corner, defeating him in New Hampshire”
That article was debunked repeatedly here since it was written. Look it up.