To try and incorporate realism behind a seemingly never ending cultural era, I believe its theoretically possible. Assuming an extremely powerful entity such as the Enclave was around in the 50s, they would've realised the attributes of that contemporary culture such as patriotism, conservatism, techno-optimism and how it would solidify the country in a potentially perpetual Cold War. Thus, through the concept of political economy, the Enclave should be able to manipulate all the major commercial bases such as the media, and continuously condition the Americans (and to an extent, the remaining Western world) to accept the 50s ideologies, values and even fashion as the dominant culture (hegemony). Meanwhile, the Enclave will do its best to filter out discourses deemed unfit to the status quo, and heavily suppress any countercultural elements. So while hippies might have appeared in the Fallout world, the Enclave probably hunted them into extinction too. Overall, it would be like how the theocracies in the Arab world have managed to solidify Islamic culture in their populaces for centuries till this day, like the above mentioned.

And they also failed to invent transistors, and color TV :brokencomputer:

Very true. The arabs still have a Medieval mentality, and obsess about things that happened centuries ago. So it's possible in Fallout the '50s mentality could have persisted for a very long time..