About 10% of all people are left-handed. About 30% of the population has a dominant left eye. In quite a few shooters, the left dominant hand is paired up with the right dominant eye, or the right hand and left eye. When shooting pistol, that mismatch is easily overcome by a slight shift of the head position. With rifles and shotguns, cross-eye dominance can be a problem. Closing the dominant eye to use rifle sights is uncomfortable and feels unnatural. Worse, a shotgunner pointing with both eyes open won’t get a good reference for the barrel position: instead of seeing the bead at the end of a rib, he might see the side of the barrel as the wrong eye asserts dominance.
One way to work around this issue is to move the head so far over the stock as to make use of the dominant eye. Most people find it awkward, but it does work. The other solution is to fire from the weak shoulder using the strong eye. Some prefer that approach, others find it trying. It is theoretically possible to re-train your eyes to switch dominance, but that isn’t a quick process.
A third way exists that works for rifle and even better for shotguns: using red dot sights. Red dot and the older occluded eye gunsights work by having one eye acquire the target and the other acquire the red dot. The shooter’s brain superimposes the two enabling precise aim. With cross-eye dominant shooters, the stronger eye looks at the target and the weaker eye picks up the red dot, leading to a sight picture as good as or superior to that of regular shooters.
Equipping a long gun with a red dot sight is a quick hardware solution to a software problem. Since many people do not want to re-train their eyes, it works out as the long-term solution for many. And for those of you who have family or friends with this issue, now you know what to put under the Christmas tree for them.