Also, there used to be, and to some extent still is, a thought that right handed shooters needed to use left wing fletching. Since most archers are right handed... etc, etc.
We now know that unless there is a clearance issue such as Jeff mentions, it doesn't matter which wing is used, they fly the same.
I did have a fellow say that at the 60 yd target he noticed he was shooting slightly to the right and that was obviously because I used right wing feathers on his arrows. I just said, "hmmmm," and didn't say anything. No sense in getting into an argument.
Guy