During the Cold War, Americans were very afraid of communism. This caused at least two major impacts on American society and culture.
One of the major impacts was the rise of McCarthyism and related intolerance. Because Americans were afraid of communism, they supported politicians and others who wanted to root it out. Those people were willing to accept it when the leaders fingered alleged communists without any real proof that those people actually were communist. This was the era of “witch hunts” in which people who were alleged to be communist could face serious repercussions simply because they had been accused of sympathizing with communism. This atmosphere of intolerance in American society was one of the major impacts of the Cold War.
Relatedly, the Cold War also contributed to the rise of conformism in American society during the 1950s. People in the US at that time did not want to seem different. In part, they feared that people would think that they were un-American and possibly communist if they acted in ways that were outside the accepted norms. The conformity that came about in American society because of this is seen as one of the major characteristics of the 1950s in the United States.