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I'm left handed, left eye dominant. I had to train myself to use both eyes, and it's a discipline that I still have to maintain through practice, otherwise I find that I'll revert to one-eye shooting by default if I stay away from the range for too long.

That said, it is easier for me to use both eyes over iron sights and RDS optics than magnified optics. There is an exception, and that is with my 4x32 ACOG which was specifically designed to be used with both eyes open, as in the Bindon Aiming Concept. I find that it works remarkably well that way. It's interesting how your brain accepts the reticle from the eye on the scope, and then either superimposes it over the unmagnified field of view, or automatically integrating the offside eye into the magnified field of view as necessary depending on range to target — making it usable at any distance from CQB out to 600 yards. So with that scope, it is now second nature to use both eyes. But with my other scopes, it is a conscious act of will each and every time, a part of my mental checklist as I settle behind the scope for the next shot to make sure that my right eye is open.

I've found though that, as my eyesight continues to deteriorate, trying to use both eyes open sometimes works poorly because I can't get both eyes to focus properly. Closing the offside eye fixes the problem. But I always try both eyes open first.