Have always shot with both eyes open...try to coach or instruct shooters to do the same...most can do it unless they have ambidextrous dominant eyes ...meaning both eyes are almost equal and left eye for a RH shooter is fighting right eye for dominance...this is where a peep is really needed...
I dont use a peep but have no issues with dominant eye or my left eye open...
if you think about it ...closing one eye is a bad deal for hunting as your losing 50% of your peripheral vision...
We have had great success on instructing shooters to shoot with both eyes open even if they shot for years closing one eye...
The exceptions are left handed-left eye dominat shooting right eye-right handed...and those that have "ambidextrous" vision and shooting with no peep...They are usually usually convinced to use the peep but still shoot both eyes open...
Then there is the rare... but more than most think...a right hand shooter with left eye dominance...again a peep is a must!
Neil