I recently engaged in a philosophical discussion on whether nuclear retaliation would be justified with a friend of mine. This left me wondering if the non- American world was similarly manic (i.e. bomb bunkers) about Nuclear war.
It depends on the time/place you are talking about — during Stalin's lifetime there was almost no discussion of nuclear war publicly in the Soviet Union, so it isn't clear what the average citizen felt — but certainly there were many who were very much aware that the Soviet Union was threatened by the United States, and from the 1960s onward there were indeed large (though inadequate to the task) Civil Defense efforts to build public shelters. (This is an area where the US and USSR differed: the US never really invested in public shelters and instead encouraged people to build private ones.)
By the 1960s and onward the Soviet people were well aware that there were thousands of nuclear weapons aimed at them. And those in the Warsaw Pact would have known they were part of that targeting strategy as well. And those in Western Europe knew that there were, by the 1950s, huge numbers of Soviet bombers and short-range missiles meant to counter their own military forces.
I don't know if I'd call any of this manic — which implies that knowing these things and being disturbed by them is somewhat irrational — but if anything the Western Europeans and (at least by the 1960s) the average Soviet/Warsaw Pact citizen probably felt this threat much more acutely than the average American. Average Americans tended to overestimate their own lack of vulnerability (and still do) to these things, which is why something like the Cuban Missile Crisis, which only threatened to slightly put the American homeland in the same situation that the entirety of the Soviet Union, China, and Europe had been in since the 1950s, led to such deep anxiety and fear. The Americans had been basing their nuclear weapons on Soviet borders for years at that point (starting in the 1950s), with plans that the American military designed to kill hundreds of millions of Soviet, Eastern European, and Chinese people over the course of hours. Your average citizen of any of these nations would not know the details of these plans but the fact that the US had built up such forces, deployed them, and was ready to use them was something that was easily known, because the Americans bragged about it.