The last bio I read of John Wayne, "John Wayne, American," did not come down conclusively on whether he "ducked" service. The authors concluded that he, indeed, had legit exemptions, but that like many others he could have lied about them or concealed them if he wanted.
The reasons keep changing according to what you read. Family, football injury, horseback riding injury, etc. Old guys that I met told me it was at the beginning of his career and he wasn't willing to risk losing ground. But all the facts can't be known. A lot of guys were enlisting. The studios might have compelled him to stay home, etc. In the end, it doesn't matter.
Don't know if it's true, but I had heard (from a former Marine - not that there's any such thing as a "former" Marine) that John Wayne, as a young man, had joined the U. S. Marines, but had washed out in boot camp.