I believe nuclear war was censored because the song came out in 2003.

FCC had temporarily banned a whole bunch of songs from live radio broadcast after 9/11 (Learning to Fly by Tom Petty, literally everything from RATM, many more) and in 2003 a while lot of Americans were terrified that Saddam would nuke us, or Israel, or terrorists would get a suitcase nuke or assemble a dirty bomb and blow up Chicago or something, as basically every journalism outfit in America was credulously reporting everything Bush admin officials were claiming about threats (which they knew were of dubious legitimacy), while the Bush admin itself was basically fabricating a claim to invade Iraq.

The uncensored version released in their album, but the music video and radio versions was censored likely so it could reach a larger audience on MTV and be allowed to be broadcast by the FCC.