It has to do with which is the "master eye". In my case, I am right-handed, but with a left master eye. I would do exactly the same (if I squinted when shooting, which you shouldn't). Having a cross-master-eye as I do (and perhaps Redford does) is easy enough when pistol shooting unless you shoot pistol like an 18th Century dueler (standing completely sideways to present a narrower target). If you shoot pistol with any modern hold and stance (
Weaver Stance or
Isosceles Stance, for instance) your body will be more or less facing the target and it doesn't matter about whether your master eye is the same as your handedness.
Rifle, and especially shotgun, shooting is another matter. With a rifle or shotgun, it is important to have your eye over the axis of the firearm.This means you either have to shoot wrong handed or wrong eyed (usually by putting a patch over your master eye and forcing yourself to use the weaker and untrained eye.
You can easily test which is your master eye. Hold a pencil upright at arm's length and,
with both eyes open, hold it in line with a distant vertical object like a telephone pole. Now close or cover one eye. If the pencil seems to jump out of line with the distant object, that is your master eye. If the alignment remains correct, the eye that you didn't close is your master eye. Quite a large percentage of the population have opposing handedness in relation to which is their master eye.
The technical term is
Ocular Dominance and there are several other methods to test this listed in the article.