I have mixed dominance, which I am sure plays a large part in my messed up perceptual/spatial skills. Right handed for writing, but do a lot of other stuff with my left. Left footed/eyed. Can't even approach my bike on the right side, like if I have to walk it, I can't do it from the right. It just feels wrong. Can only do the water bottle with my left hand, and even that is shaky. When I go down stairs or hike, I use my left foot first, although with running, I switch between both. Thus, I clip/unclip left, although I swear, I started with the right and switched after I read something, which I can't remember. I can unclip right on my mountain bike, which is more for survival, I think!
In the end, it really doesn't matter. Although I pretty much cannot ride without being clipped in. My feet fly off of the pedals and I find it very hard to get started.
I can't imagine unclipping with both feet every time I had to. I am not sure how I would get off the seat and I imagine myself impaling my nether regions on the saddle! The process of unclipping, slowing, and putting my foot down is so automatic and fluid. I really do not feel like I am leaning the bike, although I must be.