I am one of the odd balls as I am actually right handed, but shoot left handed. It was not done by choice, but by necessity.
To keep a long story short, I suffered a injury to my right eye around 15 years ago that left me with a small blurry spot in the center of the vision of my right eye. As long as I have both eyes open I do not see it and it does not effect me at all. The only time it comes into play is if I close my left eye and try to look with just my right (such as aiming a gun). So I had to learn how to shoot left handed, as I did not have a choice.
Shooting pistols is no big deal as I can still hold them right handed and just aim with my left eye.
99% of all the shooting I do is off a bench (the other 1% is pistol shooting). I rarely shoot offhand, so shooting right hand guns left handed does not bother me at all.