I never even thought about this until you mentioned it. I keep both open, though the camera often blocks the one eye. I make no effort to close one.
On occasion, though, I will position the camera so it's not in the way if I'm trying to capture movement or am walking and taking pictures - sometimes it's good to see more than the viewfinder shows.
I seem to have a preference for the left eye through the viewfinder, but it is not exclusive.