I have non-binocular vision, I shoot with both eyes open, can shoot either left or right eye, and left or right handed. I'm an extremely good shoot as my vision is unimpaired by the stereoscopic vision. When I used to do target shooting only my breathing affected things, you could hold a ruler vertical to a 10 shot grouping, and every hit would be lined up perfectly in the verticle axis.
I write left handed but and my strong eye is my left eye.