The game takes place as how people in the 50s thought the future would be like.
I just wanted to repeat this to settle that point. The reason people would be wearing 50's style pre-war clothes is because in the Fallout series the war happened when the society was wearing those clothes. It didn't happen in the 50's, it happened in 2077; however, those were the clothes they were wearing.
Fallout is real, not a simulation.
As much as some of the things in the Fallout series can boggle the mind, can you imagine if every single Vault was connected and running the exact same simulation in one long continuation of itself? It might as well be the Matrix. That gives the Matrix too much credit though, Fallout is better and real.
Edit: Real in the context of the thread, not in the context of I'm going to go out and take down some super mutants.