While it is always preferred to keep both eyes open when shooting, if someone has cross-eye dominance, it usually is impossible with iron sights. Scopes and red-dots, not so much. I shot for several decades before I even heard of cross-eye dominance and learned to shoot open sights by closing my left(dominate) eye. Seems this is a big no-no in the shooting world, You either have to switch which hand you shoot with or quit and go home. I just continue to close my left eye when shooting. I do use a dot on my glasses when using a shotgun for upland game.(basically, the same thing as closing your eye). A young or new to the game shooter, I would try to switch hands before they develop the bad habit of shooting cross-eyed. Old fart like me or someone who has been shooting for a while, I say let them close the off side eye or use a scope.