It appears that Dr. Seuss was the author of a string of political cartoons calling for action against foreign threats to the U.S.; such as, the Nazis and the Japanese. He also illustrated a number of cartoons reprimanding the American “gutless” man. I’ve included some of these illustrations below:
So, as I had suspected, “The Butter Battle Book” could definitely be interpreted to speak to a further cause than just for the education of children about nuclear war. And the message the book is portraying is something along the lines of “get up, and fight!”. In consideration of some of Dr. Seuss' books and political cartoons, he did indeed, "go to war".