I wonder if it could have anything to do with which is your dominant foot more so than your hands? I am dominantly left footed and have the bag on my left side because I prefer the weight on that side for my duffle bag. It is complicated as well because when I was little I used my left hand for everything but was told to use my right. Just curious if you guys have noticed which is your dominant foot because maybe it is preferable for which side the weight is going on.
I’m ambidextrous in the sense that I can throw accurately with either hand, can use both lefty and righty scissors, etc. but I favor my right hand for some activities (like writing - I can do it with either but usually use my right).
I tend to wear shoulder straps and backpack on my right shoulder.
I switch back and forth with any bag …my shoulders get tired easily
My shoulders slope downward. My purse goes on either shoulder, but through the years I’ve learned to unconsciously raise my left shoulder to keep the purse on, so it’s usually on the left.
Same. I’ve switched off to give my shoulder a break, like when carrying a heavy laptop bag, but I instantly hate it and it feels wrong.
I agree with your hypothesis, and also have been forbidden from wearing a bag strap across my right shoulder since surgery–they don’t want the lymphatic pathway to be compromised.
I am mostly right-handed and wear it on the right but more towards the read/hip. This allows me the best hand movement and balance/comfort on my motorcycle (my usual time to use one) and keeps my hands clear in case I need to defend myself against zombies. 
Right handed, and I usually put the strap on my left shoulder with the bag on my right hip. I read that it is better for your lower back to have the bag across the body like that and it makes sense.
Ambidextrous, but left-side dominant (I’m left eyed, left eared, left footed, and use my left hand more than my right). I can’t use left-handed scissors to save my life.
I prefer to have a shoulder bag on my left shoulder, but the door to our apt swings out right to left. There’s a crash bar on the door, and it slams shut so quickly that it often has the effect of pulling down on my purse so I can’t step up into the building. One more reason I hope to move out by May.
Right handed, usually wear them over the right shoulder. But if the bag’s particularly heavy and it’s a relatively long trip, I’ll switch from side to side a couple times.
I wear crossbody bags. They are slung around my neck and under my left side. I am right handed but consider this carrying the bag on the left.
Left hand dominant (writing, using fork), but fairly ambidextrous in every other way. If i am carrying a shoulder bag, it is usually on my left shoulder (until it gets tired, then I switch). If I wearing a cross body bag, it always goes from strap on right shoulder to bag part resting on left hip.