We cannot know for sure why countries come to have the cultures that they have. However, historians do try to explain cultural change. In the case of the Cold War, it is typically said that the Cold War helped to bring about conformity in the United States in the 1950s.
The basic argument here is that the Cold War made people not want to seem different. During the 1950s, there was an intense fear of communist subversion in the United States. This was the time of the Hollywood blacklists. It was the time of Joseph McCarthy. During this time, Americans who did not act in the proper ways might, it was feared, be seen as communists.
At least in part because of this, people came to be more conformist during this time. In order to avoid looking as if they might be communist, they tended to try to act in the same ways that other people acted. In this way, the fear of communism is believed to have helped to make the United States have a more conformist culture in the 1950s.