In addition to the above factors, African-Americans had become much more of an economic force during and after World War II, and this made their efforts at boycotting much more effective. It forced segregationists or those on the fence to consider how much they were willing to sacrifice in terms of their own businesses, and in many if not most cases, the almighty dollar trumped age old feelings on race.
We also cannot overlook the importance of television, a nearly instant and national media that brought the ugly face of racism into Americans living rooms each night. It made it harder for some to ignore the need for civil rights and motivated the younger generation of whites and blacks to actively work in favor of it, such as they did during Freedom Summer in 1964.
Lastly, let's not overlook the changing viewpoints of the court system, especially at the federal level, which time and again ruled that segregation was unconstitutional, reversing longstanding pro-Jim Crow rulings that had come before the 1950s.
I assume that you are asking for things that helped the movement succeed. Here are a few:
- The rhetoric of WWII helped to make people think about race and racism. The US talked about how we were superior to the racist Nazis. This helped push the idea of civil rights into more people's minds.
- The US needed to gain the approval of black and brown people around the world because of the Cold War. The US was competing with the USSR for influence in the "Third World" which was mainly made up of people of color. Segregation and racism looked bad so many American leaders wanted to do away with them so we could look better in the eyes of nonwhites.
- During WWII, many black Americans moved north to work in factories. This meant that they were present in large numbers in places where they were allowed to vote. This made more northern politicians receptive to the idea of black rights.
There are many other things, but these are some of the important circumstances that made white America more receptive to the ideas of the movement.