Liberal democracies, for the most part, I don't see any problem with them having anuclear weapons, because liberal democracies pretty much only have them for deterrance purposes. You don't allow rogue nations controlled by maniacs to have nukes however, for the same reasons you do not allow the murderers and rapists and terrorists in society to own guns.
Big nations, like the Soviet Union or China, these you really could not do anything about, but at least when dealing with something like the Soviet Union or China, you knew/knoq that you were dealing with a government, not a country led by one maniacal leader who might do who-knows-what.
Many nations fear Iran having a nuke I believe because Iran historically has been an expansionist-hungry country.