If I recall correctly King was involved in the Birmingham bus boycott. That aside, Blacks did not have the legal right to stay at a motel, eat at a lunch counter, much less buy a home in a non-Black area until the mid 60's. Even then, they were not always able to do so even though to refuse was against the law. King was the most memorable speaker at the march on Washington prior to the passage of the 64 Civil Rights bill. By 68, he was getting sidetracked into Vietname Anti-War movement.
That was only true in the South.