“Go save the Jews” was hardly a motivating factor for any nation in the war.
IDK if things have changed but generally the whole narrative in the US is presented as unwitting yankies discovering the horrors of the death camps. It's debated how much some levels of the government knew, but it certainly wasn't public knowledge in the US.
Well, that or fighting the Japanese.
Patriotism and threat seem to have been the main motivators for most people in the west.
Difficult to pin something as all consuming as WW2 on "about" anything, but we can look at who fired the first shots, which was clearly the Japanese invasion of Manchuria in the east and the German invasion of Poland in the West (followed shortly after by the USSR invading Poland and later Finland from the other direction.)
It is not at all a given that, had Germany stayed within her international borders, that the Holocaust would have on its own triggered WW2. After all, mass murder in the Congo Free State didn't trigger invasion of Belgium.
Many people in the British Empire were told to fight for the mother country or even to preserve the empire (which was largely gone by the seventies, with some major territories becoming independent in the later 1940s.)