If there were a WW3, then it'd be difficult for countries to remain neutral.
Look at the Cold War, who was neutral there? Not many.
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Of the neutral countries, China wasn't, it participated in the Korean War on the Soviet's side, though it didn't particularly like the Russians, so didn't get involved in much of the later stuff, mostly because it was too poor, like India.
In fact every country that didn't participate was probably because their poverty wasn't an asset for the US or USSR.