I'm left eye dominant but right handed. The simple solution is to close your left eye as you mount your gun. Or close it when you call for the target if you're shooting clays.
Had I realized that and its implications earlier, I would have switched to shooting left handed. (Not only is my left eye dominant, but I have slightly better vision than in my right eye.) Try doing that after you've been shooting right handed for decades and you'll find that it's incredibly awkward. It's not so much of a problem when the gun's at your shoulder, but adjusting to everything else including loading etc feels really strange.
Cataract surgery on my R eye several years ago initially helped my shooting. Then things started going downhill. Turned out I also had macular pucker in my R eye. Depending on light conditions and the background against which I was shooting, clays (or whatever birds I was hunting) would be visible if silhouetted against the sky. Against something like trees, there was a good chance they'd flat disappear. After I had the macular pucker taken care of, that solved probably 90-95% of my problem.
