I have always been right hand/left eye but only time it ever mattered was when I would win bets shooting modern firearms "handycapping" myself by shooting left handed.
With archery I shoot both eyes open and look where I want the arrow to go, not down the string so never really thought about it until a few seasons ago at a 3D shoot.
I have been practicing with my dual shelf Bear recurve to try to get more comfortable, but still like to carry my bow in my left hand so I have the right one free to use calls, look at my GPS, and other items.
Whatever is more comfortable for you..
If it works, dont (?) with it.