Seeing two barrels, when the gun is mounted into the shoulder and both eyes are open, is not ocular cross dominance! It is called natural diplopia.
The phenomenon occurs because the object (the gun) is too close to our eyes compared to
the distance from our closest focal point. The closest focal point is where the two eye axes intersect at the closest point, also called the first focal point. If the object is closer that this focal point, the shooter perceives both images from each eye.
The two images are formed independently. The image from the dominate eye is the real image, the image from the non dominate eye is the ghost image. When learning to shoot with both eyes open we try to ignore the ghost image.
Shooting with binocular vision(two eyed shooting) is the best for shotgun shooting. Considering that we shoot upon mobile targets, it is very important that the brain compiles the visual information from both eyes.
When we close one eye, the ghost image disappears but at same time we cut the binocular vision to monocular vision(one eyed shooting) eliminating the depth perception as well.