I am left eyed, and right handed. I have shot extensively in the military, competition, and recreation and always shot right handed rifle or pistol. I never knew there was a difference or that it mattered until someone mentioned it and I realized I was LERH. Still, I have no issues, and I think the "problem" is overblown. I shoot scoped/iron sight rifles with my right eye, red dots with both eyes, and pistols with my left eye. It all feels natural, and I do well in all respects. I actually think it may be benificial with red dots as it is very easy and natural for me to use both eyes. I even shoot both eyes open with magnified optics and irons. I can also shoot off-hand pretty well, but I'm terrible at it when it comes to reloading and other non-shooting gun handling.