Wayne was in his early 30s when the war broke out, which is "old" by army standards. But many famous athletes, directors, and actors volunteered nonetheless -- and some of them were much older than Wayne, with some even lying about their age to serve. Both Jimmy Stewart and Clark Gable (in his 40s) signed up for bombing missions over Germany. But the Duke avoided service in any way possible, confessing "I better go do some touring -- I feel the draft breathing down my neck."
It's not clear why he didn't use his connections to get a job behind a desk or to make training films. Whatever the case, he was well aware that doing this carried a stigma. At a publicity tour at a hospital in Hawaii, Wayne was booed by wounded Navy personnel who got annoyed by a phony macho guy trying to give them a pep talk. Evidently, Wayne never lived down that humiliation. Which is saying a lot for a guy who voluntarily starred in The Conqueror.
RKO Radio Pictures