I don’t think that there can be any doubt that (for most of his life at least) Churchill was a “white supemacist”. It went with the terrority if you thought that a European state should have a colonal empire. Of course he was not alone. All supporters of the British Empire were white supremacists as were those of the French, Belgian, Dutch, Spanish and Portuguese empires and those in Germany and Italy who thought their state should have one too.
It is also true that the Second World War was one between the British Empire and expansionist Germany, and at the start was presented as such by both sides, though later the rulers of the British state decided that this wasn’t a good way to retain popular support for the war. The rulers of Germany, on the other hand, played to the end that card for all that it was worth. As for the American state, when it joined in it fielded a segregated army.
The Doctrine of Discovery is more than, it gives to the white men the right to kill other ethnic groups because they are inferior, and to take their territory, their wealth, and their possessions, it is the maximum expression of white supremacy and it is still being applied and used by several countries including the USA