The way I reconcile the whole 1950s theme of Fallout is cultural regression. Consider the state of the US just before the bombs dropped: China is on the warpath, the US has annexed Canada, nukes are aimed and ready.
To keep control of the populace, the government began a massive (starting years before in anticipation for nuclear and other conflicts) propaganda campaign.
This campaign included sticking advanced, miniturized technology (like tiny supercomputers) into clunky robots and big retro computers. People dressed like those from the 1950s (although the fabric was completely synthetic), listened to “record players” (not your common vinyl, though), and drove “gas powered cars” (really, energy cell powered).
Social progress was dismantled, and institutions like the Elks club, etc., re-emerged. The internet was banned, then forgotten.
So everyone played the part of the placid 1950s, leave-it-to-Beaver family. All the while, the US had become a police-state.
It was sort of like how Hitler invoked the whole Tutonic Knights thing with made up ancient Nazi regalia.
That’s how the 1950s theme will be reconciled for this campaign (not that your characters are aware of the history, though—really I wrote this to add to the “suspension of disbelief”).