As history enthusiast you realise that MLK's demands have not been new. Sudden was how the powers that be have suddenly caved in to some of these ancient demands. Why did that happen?
In Russia it's believed to have been caused by constant Soviet criticism in the UN which made America look ugly in the eyes of world's "progressive intelligentsia". We say: "that's why they acknowledged, of all people, MLK! He was religious and completely not a commie." This is also how we explain affirmative action: Lyndon Johnson and Nixon are believed to have done it to create a token black middle class to stop us from shouting "look how unjust you are! You still can tell the former serfs and former landlords by the color of the skin!"
But the internet taught me that people often see their own, national, statesmen at the crux of world's affairs. American historians will not agree that Khruschev singlehandedly abolished American racism any sooner than their Russian colleagues agree that Reagan somehow singlehandedly abolished the USSR.
So how do the serious American historians explain the sudden change of attitude towards their caste of manumitted slaves?
First, I would like to address the idea that the cause of the victories of the Civil Rights Movement might be attributable to any outside, international force: the root causes of the Civil Rights Movement are deeply internal, with complex, interrelated strains stretching back to Black veterans returning from World War II, to the shift in demographics leading to the migration from the rural South to cities across America, to the legacy of post-Civil War Reconstruction policies, even to the Abolitionist movement leading up to and after that war. To assert that there was some “sudden change of attitude” in mid-1960 is to misread the history.
What you see as “the powers…suddenly caving” or some “inversion” of public opinion by White Americans toward Blacks is a Much more gradual force.
One strain of the Civil Rights Movement can be traced, partially, to the early-20th century labor movement. These were militant, well-organized and had African Americans in all levels of leadership. This was very fertile ground in which later grass-roots movements might grow. Returning Black veterans from World War II were another source. They were well-trained, organized, had made dear sacrifices for the nation, and still encountered racism and segregation upon returning home. The implications of Fascism – especially the Nazi persecution of Jews – had been clear to African Americans, and throughout the war, they and their labor movements wedded the war effort overseas with an end for racism back home. There were ample parallels between anti-Semitism and racism. The revulsion which the Holocaust produced in Americans was easily used to undermine Jim Crow. Everything taken together, and Black political activism soared. The Fair Employment Practices Committee was established in 1941 (putting racial discrimination on the national agenda for the first time since Reconstruction); the exclusion of blacks from primaries ended in 1944; major voter registration drives sprung up across the South; the military was desegregated, as was graduate education.
All of this lay in the background when, in 1955, a 14 year-old boy from Chicago, named Emmett Till, was lynched in Mississippi by rural whites for the offense of flirting with a white woman – sparking, in the eyes of many historians and lay folk alike, the "Classical" Civil Rights Movement, and a specifically moral strain of it (opposed to the largely economic previous strain) led by Black Christian leaders.
Reasons for its success include all of the above events leading up to it, as well as other aspects unique to this incarnation.
Urbanization, the migration from the rural South to cities in the South, North and West, played a large part, and this process accelerated after World War II. This transformed the “racial geography” of America, forming interconnected networks which crossed the boundaries between rural and urban America, ensuring that developments in one region would cross into and affect the other. Struggles in the city and in the countryside could now be mutually reinforcing.
The eminent use of non-violent protest and civil disobedience, resulting in violent reactions, which in-turn was captured and amplified by the media (aided by the new technology, television), launching an outcry throughout the nation against such atrocities – an outcry which could not be ignored by "the powers that be". This forced the hand of the Federal Government – who could ignore neither the public outrage, nor the blatant humanitarian crisis – who responded by throwing their full weight into the fight against Segregation and overwhelming local governments who stood in the way.
Another reason for the successes in the 1960s was the unique and powerful coalitions which had been formed, across racial, class and political boundaries, which included labor unions, civil rights activists, New Deal politicians, and a multiracial youth base deeply engaged in broad shifts in society and culture. This took time to develop.
This all took time to develop. That Cold War “games” being played for public opinion were the true impetus fail to take into account any of this. Reagan did not bring down the Soviet Union; and Kruschev was not responsible for America’s Civil Rights victories, nor did he sway the minds that were.
The idea that America’s perception by the international community regarding the “black spot” of the racial violence and injustice going on within its borders does have a place within the history of the Civil Rights struggle. But it is limited. I remember listening to a related NPR piece: visiting dignitaries from newly-independent African nations would arrive in a Southern city (Atlanta? Some Southeastern city which was commonly flown into) and, attempting to check into a hotel room, were shocked to be turned away because they do not accommodate Blacks. Nice restaurants would not serve them. These dignitaries would arrive in Washington incensed by how they were treated thus far. And this was the prime period in the Cold War when the competition between America and Russia over the loyalties of all of the de-colonized African countries was fiercely contested. So the Federal Government put some pressure to the Southern governors and mayors, demanding something be done about their Segregation laws.
But you're post makes Dr. Martin Luther King Jr sound like he was a government stooge, a mere pawn; as though he were some religious nut easily manipulated by the more organized and more efficient powers-that-be. If that is what Russian children are being taught about Dr. King, I am very sorry to hear.