I assume that you are talking about the post-WWII era here. If so, there were challenges to the dominant culture from both right and left.
There were, for example, the "Beats" who felt that modern culture was excessively materialistic and lacked any spiritual aspect. There were African Americans who felt left out of the new prosperity and fought to get a part of it. There were conservatives who were concerned with the push by black people, but also by things like rising juvenile delinquency and with the effects of things like rock-n-roll music. In this way, there were various movements that opposed the dominant trends.