Concomitant to the Bomb was, of course, the cold war – and clearly that, too, influenced the book. The Soviets were sending writers to gulags and banning questionable books, while in the US McCarthy was persecuting writers and the HUAC was in full swing. And then, of course, the memory of the Nazis still burned all too bright.
Well, actually, HUAC was busy mostly in the 1940s and McCarthy investigated the State Department and the Army, not writers. As for Bradbury and Fahrenheit 451, he goes into that here, to wit: "Bradbury, a man living in the creative and industrial center of reality TV and one-hour dramas, says it is, in fact, a story about how television destroys interest in reading literature."
The 1950s were like any other time, a mixture of good and bad, fresh and stale. I remember nuclear drills in school, when we got down under our desks. I don't remember many of them, though -- only one, actually -- but I do remember that none of us thought about it very much. Great way to interrupt the school day. For me, the good and the fresh outweighed the bad and the stale. Interestingly, it was first time I heard alarms being sounded about the federal goverment's fiscal incontinence. Subsequent decades certainly dealt well with that, didn't they?