I would disagree with Bjorn.  In any sport with two eyes open, if your aiming eye is not your dominant eye, your brain will thow you off target by calibrating throug the dominent eye.  
I say this having shot skeet, trap, and instinctive archery for over 40 years.

At one point I taught archery.  Since I'm a lefty and was required to shoot right, the only way for me to consistently hit the target was to close my non-aim eye.  This, to my thinking, would be a handicap in hunting.

With rife shooting it doesn't matter, because one is taught to close the eye not used for aiming.

My grandfather taught me to shoot both eyes open; rifle, pistol, and bow.  Works for me.

I was born left handed. My left eye is my dominant eye. I write left handed. I throw a ball left handed. I shoot a gun left handed. Here's the strange part. I'm 58 years old and I swing a golf club and baseball bat right handed. I have shot a bow right handed since I was a little kid. Those 3 things just feel natural just as the things I do left haned feel natural. I shoot with both eyes open and never even considered switching to lefty for a bow. I know that is supposed to be the correct thing to do but I figure if it ain't broke don't fix it.