The original question had to be edited. I think that the American consciousness in the 1950s was conditioned to believe in the classless society for a couple of reasons. The first was that such thinking enabled Americans to focus their energies on being "successful." In stressing that there were no social stratifications or barriers that inhibited success, Americans could work hard, achieve externally defined contours of prosperity, and not have to ask questions about why they did what they did. The idea of Americans becoming "other- directed," or driven towards achieving social values that were emphasized by media and institutions was enhanced with the notion of a classless society. The perpetuation of this myth helped to driven the prosperity of the time period.
At the same time, the advocacy of a classless society allowed the machinery of capitalism and profit driven motives to progress without any dissent. Those who were marginalized by this system such as people of color, women, or those deemed as "different" were silenced. They were seen as aberrations or failures. In being able to continually argue that there was not a class system in America, it became easier to criticize these individuals as simply being "whiners" or individuals who did more complaining as opposed to actual working. Discrediting and dismissing these individuals became easier in a social setting that was classless. The use of the opportunity ideology in this condition helped to perpetuate this silencing of voices.
Finally, the driving of American society with the aid of a classless construction helped to define it more easily against the Soviet vision of reality. "Classes" in society was used to be a Communist construction. American society's notion of "classlessness" was used to define itself in stark opposition to the Soviet Union. The fear of Communism and its paranoia that infiltrated so much of American society of the 1950s can be seen in the need to assert itself as classless. In defining it as such, Americans who embraced a classless vision of social self were "true" Americans. Those who advocated the opposite point of view were cast as "outsiders" and "Communists." Given the Red Scare of the time period, this became another reason why many Americans were conditioned to think of themselves as part of a classless society.