I'm no olympian, but squinting one eye shut can mess up your vision when aiming. Leaving both open takes some extra attention away from the target. I don't shoot competitively, but I leave both eyes open. I assume the same for them.
I teach drawing and my students are required to measure alignment of objects using their pencil as a straight edge whilst looking through one eye. Some students have trouble with this and have to place one hand over there non dominant eye.
Since I lost my left eye I have no trouble looking through only one eye. However, I have acquired plenty of troubles with balance.
I'm not a shooter, but people do the same thing when looking through a telescope, or a microscope with one eyepiece. You learn to ignore the other eye.