As I understand it, you are not required to touch on all of the events you mention in this answer. I will discuss the Cold War and social reform with reference to McCarthyism and the Civil Rights Movement. The Immigration Act of 1965 will be mentioned briefly in the discussion of the Civil Rights Movement, but the phenomenon of suburbanization seems to me to be only tangentially related to the Cold War.
In one way, the Cold War made social reform harder to achieve in the United States. During much of the Cold War, anyone who wanted to make changes in American society could be painted as a communist or a communist sympathizer. Because of the political and social climate created by the McCarthyism of the 1950s, many people were wary of being tarred as “red.” For that reason, fewer people were willing to push for real social reform.
Conversely, however, the Cold War is often credited with helping to bring about one of the most important reforms of the 20th century: the extension of civil rights to African Americans and other minorities. Historians say that the political needs of the Cold War induced some American leaders to promote civil rights. These leaders felt that it looked bad for the United States to be oppressing a group of its citizens when it was trying to promote democracy around the world. It was particularly bad for the US to oppress brown and black people when it was trying to woo countries in Asia and Africa to its side of the Cold War. This same logic might have been somewhat helpful in bringing about the Immigration Act of 1965 since it tore down racist immigration policies.
In these ways, the Cold War helped to promote social reforms in some ways, but hindered it in others.