In my training by the NRA National Coach Staff the dominant eye is not a factor in stationary target shooting, if both eyes are of a similar acuity. The old way was to force a shooter that was (for example) right handed but left eye dominant, to change hands and shoot left handed. This is usually a very frustrating situation and many young shooters quit the program. The new theory on this is that the shooter keeps his right handed style and the dominant eye is occluded or covered by an opaque occluder. We use Scotch Magic tape on our glasses, to cover the dominant eye. The reason the occluder has to be opaque is to allow light to enter the non-shooting eye. If you close the non-shooting eye or use black tape to cover it, both eyes will dilate and you lose your sharp vision. The smaller the pupil of the eye, the sharper the vision will be.
As far as bi-focals, they are not a problem for me using iron sights on a rifle. I look over the top of the reading bi-focal. As far as pistol shooting is concerned, I raise the bifocals with a device that allows me to look through the reading part of the bi-focals. This puts the front sight in sharp focus and the target is a blur as well as the rear sight. Better shooting is done that way. Of course the tape and lifted glasses are for target shooting.
As far as telescopic sights are concerned, I do not close my non-shooting eye. I have trained myself to disregard what the non-shooting eye is seeing. You can actually switch back and forth and follow a deer with the non-shooting eye, then switch to the shooting eye to make the shot.
I keep both eyes open when shooting moving targets such as trap or skeet. It is important to have bi-nocular 3D vision in moving targets. A trap shooter with a dominant non-shooting eye , should try to train himself to change shooting styles, so the shooting eye and shooting style match, such as right handed shooting right dominant eye.