I am left eye dominate and shoot right handed. If shooting with one eye open the shift to the left to accommodate using my left eye is so minimal that it is not noticed. When shooting with both eyes open it just plain doesn't matter.
I taught a left hander to shoot handguns. I taught him to shoot right handed because the majority of all handguns, an everything else in the world, is designed and oriented for right hand operation. With the arms at full extension he never experienced any issues.
Shooting a rifle or shotgun is where the problems arise because of the nearness of the sights to the eye. Also there is the relative scarcity of long arms designed to be operated with the left hand.