The former interevened during the great Depression and earlier because they wished to defend our system of democratic capitalism.
How in the world can you compare their motives or actions to anything Hitler did?
You were the one who suggested the Gold Standard: they all "meant well."
Easily - they bear comparison. I would certainly understand your objection to comparing them with everything Hitler did. FDR was not Hitler (no mustache) but both of them presided over a period of recovery from economic crises. Their means bear studying.
Each is an example of state intervention to rectify economic depression; in Hitler's case it was a depression following a period of hyperinflation and largescale flight of capital. Hitler's priming of the armaments industries came before FDR was obliged by world events to follow, but both injected government money into a moribund manufacturing industry even outside of armaments, created jobs by doing so, and generated satellite manufacturers. It wasn't, properly speaking, a "Keynesian multiplier" because of the disposable nature of the final product; tanks, once made, generate little further wealth. But it did begin a bubble of expansion.
Where did the actual capital come from? Mostly it was simply printed up by the respective governments, hardly a recipe for permanence, and in fact both countries would have faced economic disaster at some point anyway had not the war placed the principal burden on the losers. Postwar U.S. industrial expansion was brisk in those areas which were either necessary for defense technologies (aeronautics, electronics, etc) or easily convertible to civilian applications (consumer goods such as household appliances and automobiles), or both. That part wasn't sleight-of-hand, it was a real increase in the production of wealth. Its surplus primed the pump for a similar process in Europe.
The point is that (IMHO obviously and subject to debate) while governmental intervention primed the pump it did not cause the economic expansion by itself. The war masked this central fact and in a truly dreadful manner created a market (if you can trivialize razing a city as "creating a market") which allowed the real expansion growing room. I suggest that it also masked the inadequacy of government to do anything but prime the pump and encouraged people that government intervention was responsible for more than it really was. There, I think, is the real playing field for debate between liberal and conservative economic policy proponents.