Wayne had an exemption because he had a large family. But he did make pro-war propaganda movies.
What I've heard from old Hollywood types is that the studio pulled strings. Ford wanted him to join Oh So Social with him and Wayne chose his career.
If you want to write a fascinating book, check out the relationship between Ford and Wayne. Some of the guys who knew them both are still around, but probably not for much longer.
Check this out!
http://www.history.navy.mil/faqs/faq81-8b.htm