What specific agencies, groups, ideas, and events help explain the success of the mainstream freedom movement (not Black Power) from the early 1950s to the mid-1960s?

Gandhi’s doctrine of non-violent resistance and Thoreau’s ideas about civil disobedience provided an inspiration to civil rights activists, especially for Martin Luther King who used these ideas to formulate his own doctrine of “militant nonviolence.” As he put it in his famous “Letter from Birmingham City Jail” (1963), the objective of confrontational civil disobedience was to “create such a crisis and foster such a tension that a community which has constantly refused to negotiate is forced to confront the issue.”
King strived to engage the conscience and foster sense of justice, fairness, and decency in his opponents. In his Christmas sermon in 1967, he expounded on a passage on non-violence from E. Stanley Jones’ book Mahatma Gandhi: An Intepretation (1948): “The weapons Gandhi chose were simple: We will match our capacity to suffer against your capacity to inflict the suffering, our soul force against your physical force...we will wear you down by our capacity to suffer. And in the winning the freedom we will so appeal to your heart and conscience that we will win you...” (as quoted in Keith D. Miller, Voice of Deliverance: The Language of Martin Luther King, Jr. and Its Sources, 1998, p. 90).
Important Supreme Court decisions in the 1950s challenged the doctrine of “separate but equal” and provided legal justification for the civil rights movement. For example, in Brown v Board of Education of Topeka, Kansas, May 17, 1954 the Supreme Court ruled, “We conclude that in the field of public education the doctrine of ‘separate but equal’ has no place. Separate educational facilities are inherently unequal.” (Full text available at web.archive.org.)
In his “Letter from Birmingham City Jail,” Martin Luther King referred to this decision as well as to the opinions of St. Augustine and St. Thomas Aquinas about the inherent injustice of laws that are contrary to natural law (which demands the equality of all people). He also followed Martin Buber and Paul Tillich in stressing the existential importance of the human personality and grounded his rejection of segregation, which reduces people to the status of objects, in their teachings. Here is this important passage from King’s letter.

YOU express a great deal of anxiety over our willingness to break laws. This is certainly a legitimate concern. Since we so diligently urge people to obey the Supreme Court's decision of 1954 outlawing segregation in the public schools, it is rather strange and paradoxical to find us consciously breaking laws. One may well ask, "How can you advocate breaking some laws and obeying others?" The answer is found in the fact that there are two types of laws: there are just laws, and there are unjust laws. I would agree with St. Augustine that "An unjust law is no law at all."
Now, what is the difference between the two? How does one determine when a law is just or unjust? A just law is a man-made code that squares with the moral law, or the law of God. An unjust law is a code that is out of harmony with the moral law. To put it in the terms of St. Thomas Aquinas, an unjust law is a human law that is not rooted in eternal and natural law. Any law that uplifts human personality is just. Any law that degrades human personality is unjust. All segregation statutes are unjust because segregation distorts the soul and damages the personality. It gives the segregator a false sense of superiority and the segregated a false sense of inferiority. To use the words of Martin Buber, the great Jewish philosopher, segregation substitutes an "I - it" relationship for the "I - thou" relationship and ends up relegating persons to the status of things. So segregation is not only politically, economically, and sociologically unsound, but it is morally wrong and sinful. Paul Tillich has said that sin is separation. Isn't segregation an existential expression of man's tragic separation, an expression of his awful estrangement, his terrible sinfulness? So I can urge men to obey the 1954 decision of the Supreme Court because it is morally right, and I can urge them to disobey segregation ordinances because they are morally wrong.

African American evangelical churches in the South found inspiration in the early Christian idea of the equality of all believers irrespective of their origin. They participated in the civil rights struggle and provided numerous volunteers and organizational support, in addition to symbols and songs, such as the famous anthem of civil rights movement “We shall overcome,” which derives from an African American gospel song. Martin Luther King and his followers created the Southern Christian Leadership Conference (SCLC) in 1957.
Left-wing students who believed in human rights and equality also enthusiastically supported the civil rights movement. They created their own organization, the Student Nonviolent Coordinating Committee SNCC (1960), which cooperated with the SCLC.
On December 1, 1955, the African American seamstress Rosa Parks, who was involved in the local chapter of the NAACP (National Association for the Advancement of Colored People) refused to give up her bus seat for a white person. She broke the ordinance of the city of Montgomery and was arrested and fined. In response, activists launched the Montgomery Bus boycott (December 5, 1955-December 20 1956), during which approximately 40,000 African American bus riders refused to ride city buses until the Supreme Court declared the ordinance illegal and Montgomery buses were integrated.
The struggle for school desegregation in Little Rock, Arkansas (1958/1959) involved the use of federal troops to enforce the desegregation mandated by the Supreme Court. President Eisenhower, who ordered the troops onto the scene, was a reluctant ally of the civil rights movement. He introduced the Civil Rights Act of 1957, which created the Commission on Civil Rights but otherwise had little impact because of difficulties with enforcement. The Civil Rights Act of 1960 corrected some of the shortcomings of the 1957 bill but also proved inadequate.
The new president, John F. Kennedy, who initially was also only marginally supportive of the civil rights movement, gradually came under the influence of King’s ideas and increased his involvement in the battle for civil rights. After the events in Birmingham, Alabama (1963), Kennedy called for the adoption of a new, more comprehensive Civil Rights Act. The Civil Rights Act of 1964 became a centerpiece of Civil Rights legislation. It prohibited all forms of racial discrimination, including in education and the workplace, and also demanded full voting rights for African Americans.
In 1963, about 200,000 Black and white demonstrators participated in the March on Washington for Jobs and Freedom, where King made his famous “I have a Dream” speech advocating a non-racial future for the American people. Another important march from Selma, Alabama to Montgomery, Alabama took place in 1965. Across the country, sit-ins and freedom rides undermined the daily practice of racial discrimination. Many activists faced violence from white bystanders and police officers. Murders of civil rights activists and bombings of Black churches failed to stop the movement.
Following the adoption of the Voting Rights Act of 1965, the SCLC was able to register 3 million new African American voters. Despite the assassination of Martin Luther King in 1968, the civil rights movement made significant advances in the fight for civil equality.