I am left eye dominate and shoot a gun left handed, but being right handed, I began to shoot a bow right handed when I first took up archery in 1958. In fact, in the beginning, shooting my bow right handed with left eye domination didn't even occur to me that it would be a problem. With a lot of practice over the many years, I really haven't had any issues with the left eye dominate/right handed combination. Because of all the arrows that I have shot, perhaps my brain has made some sort of adjustment that has allowed me to maintain accuracy.
I use both the open and square stances when I practice because I feel in actual hunting situations, you may need both. When using the open stance, I need to make sure I keep my right elbow tucked in and not let it fly out. This insures a good crisp release.