To what degree did military and political objectives correlate for the US in World War II?
For the great bulk of WWII, the political and military goals of the United States were practically identical.
In this war, the US was not really trying to remake the world. All it wanted to do was to defeat Germany and Japan. This was, of course, its military goal as well.
Towards the end of the war, the political goals expanded. The US started to look towards a possible Cold War with the Soviet Union. It started to look to rebuild and reform Germany and Japan. But these were not goals that were being contemplated for most of the war. For most of the war the political and military goals were identical; the US was simply trying to defeat the enemy.