I always try to stay to the right. I see it as the correct side to be on, though it's probably because of driving. I also feel the same as you about not wanting people passing too closely to my strong side. I have found a nice way to stop that feeling of people getting too close to my firearm. I keep my right hand in my right front pocket. It's only the 4 fingers and from the middle knuckle down, but it keeps my arm constantly on my firearm. It's kind of a way of keeping better retention and quick access for myself.