It is comparatively easy to sort out WWII's 'war of weapons' (particularly if one is allowed to view that war moment by moment, region by region), much less so for its 'war of ideas'.
True, the weapon war has its classification difficulties.
After all, many countries that were originally Germany's friends on the battlefield (such as Italy, Russia, Hungary and Finland) eventually ended up being savagely attacked by their erstwhile friend.
Even Britain seriously thought about bombing Russia ---- but then later decided to sent it bombers instead.
(We also mustn't forget that originally Britain fought side by side with the French military, only to kill thousands them at Oran Algeria in 1940 and then by late 1944 was once again fighting side by side with the French.)
And of course, not so very long after the war, Germany became Britain's new bosom friend and Russia its new sworn enemy.
The cases of France, Italy and Hungary reminds us that for many (perhaps even for most) nations, WWII was often as much a deeply divided civil war, fought over ideas, as it was a war of weapons fought by the entire (fully united) population of a nation simply intent on resisting foreign invasion.
But fundamentally, I believe that WWII's war of ideas was mostly fought, almost invisibly and mostly silently and inaudibly, inside billions of individual minds.
Over the seven long years of the war and its immediate aftermath, most people became far less certain than they were in 1939, about a collection of unexamined assumptions that we now call Perfectionist Modernity.
It was proving far harder than once thought to perfect perfection and there were increasing doubts that the version of perfection that had been put about really was perfect.
Humanity, Nature, Reality ---- they all proved to be far less amenable to suggestions from 'the smartest civilizations in the Universe', than anyone suspected.....