So was Harry Blackmun. So is David Souter.
King may technically have been a Republican, because it was probably impossible for a black to register as a Democrat in Georgia in those days. But it's a non-starter to try to make the case that King believed in Republican principles. He did not. He was a socialist. He supported the enemy in the Vietnam War. If he were alive today, he'd be calling Bush a fascist and supporting Hugo Chavez. After King's death, Coretta King became a fixture at Democratic conventions. His allies (Jesse Jackson, John Lewis...) became Democratic Party regulars.
Blacks aren't going to vote Republican today because of the Democratic Party's anti-black attitudes decades ago. It's a waste of time dwelling on it. Blacks know that the Democratic Party today panders to them. Expecting them to vote Republican today because of the anti-black actions of the Democrats decades ago is like expecting southern whites to vote Democrat today because General Sherman and the Carpetbaggers were Republicans.
I'm not disputing your history on this, but it seems to be a daily routine here for good, decent folks like yourself to expect blacks to flock to the GOP because some Democrat was a klansman 87 years ago. Not gonna happen.
King ran voter registration drives. He could register however he wanted to... He didn't support the enemy in Vietnam, but he did not support the war. And like JFK, King had a lot more in common with today's conservatives than he would ever have with today's whacked out liberals.