I've tried to shoot with both eyes open on several occasions, I can, but not fast and definitely not on a moving target. From my teaching (NRA Rifle, Shotgun and ML'ing Rifle Instructor, mostly for BSA), the kids with perfect vision could do this pretty easily, the kids that had to wear glasses had a VERY tough time keeping both eyes open.
For instance, I'm a glasses wearer, if I keep both eyes open, and keep my front sight focus, I literally have two targets. At 10 yards, the targets are several feet apart. With practice I could probably get good enough to trust to hit the correct one at speed, but squinting one eye is pretty natural for me (boxing and martial arts do this a lot with incoming strikes).
I only close the eye to line up the shot, the rest of the time it's both eyes open and scanning for targets, identify, close eye, bring gun up, fire, open left eye and scan.
YMMV.