The issue of eye dominance applies onlt to binocular vision. You are a good rifle shot because you are using only your nondominant right eye in a monocular manner. You can produce the same effect by closing your left eye when handgun shooting, although that is frowned upon, and for defensive purposes unwise to occlude nearly half your field of vision.
Eyeedness can be switched. It involves wearing an eye patch over the dominant eye long enough for the brain to reprogram to make the other eye the dominant one. I don't know how long it takes, but you get to look like a pirate for awhile and can shoot without difficulty in the meantime.
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