I have a good friend who is right handed/left eye dominant. Well, now that I type this I can think of 2 toher friends who are the same. All 3 of them shoot either right or left handed.
I have some physical limitations and shoot off of whichever shoulder I am able to at the moment (I am right hand/right eye). At times I am physically able to shoot off of either shoulder, so I just pick the one that is easiest for that particular shot.
If you teach him to shoot from each shoulder, he will be a better hunter.
One thing I have noticed is that I would say 80%+ of the people I have met who were cross eye dominant are women. I have often wondered why that is. There must be some advantage to it or those genes would not be floating around in the pool.