And this fits into the picture how? Did this stop cities and municipalities from making unconstitutional laws which treated blacks as subhumans as did the Taney court?
No it didn't. The 14th amendment didn't mean crap. And those laws were only repealed when blacks in the south stood up to the tyrants and told them to take their laws and shove them. I know you'd like to think that blacks in the south grovelled in front of legislatures and said "please massah, may we use the good toilets and ride on the busses with the white folk, pretty please?"
But that aint the way it happened. They disobeyed.
How? It makes a mockery of your assine claim that such a law as that promoted by MLK would have been laughted out of the state's legislatures. The very fact that a constiutional amendment to that effect was passed by 3/4 of those very legislatures 100 years before MLK shows you have absolutely no understanding of any part of our country's history.