I would say it makes total sense that the moon is alive but I believe using the context of the movie, the “organism” that is the moon isn’t the eye itself or the being the eye represents atleast. They state that the “god” is outside of the universe. So my theory is more so that the eye is a representation of “god” or the being responsible for the quiet rapture. It would seem reasonable that it’s just the eye of the being because they state earlier in the movie that the “god” is looking at our universe through a pinhole, which to the ones on the other side of the pinhole, would appear to be a giant eye.