Well, I don't mountain bike anymore, but I am so dominant left side when it comes to cycling, it's probably dangerous. I can't even walk my bike on the right side. It just feels wrong.
I am right handed, but I mount and dismount, unclip on my left. I start off with my right foot clipped in, but that's it. When I was mountain biking, I practiced unclipping on the right and I could do that if needed, but on the road, no way. I know when I started riding I was unclipping right, but I changed for some reason, and now I can't do it on the right side anymore. I can't really take my right hand off of the bar, either. I can only drink with my left hand and I can barely signal to make a right turn with my right hand... I do, but I often wobble, or its it's at the beginning of a ride, I am shaky.
I've been riding for ten years and it's not getting any better. I just deal with it. I know my balance and spatial skills suck, so it's not like I haven't had time to practice.