It's not perfect refraction like a prism. The peculiarity of our planets atmosphere's molecular makeup means blue is refracted more than any other color and is captured by our atmosphere - hence blue sky. And why we must daylight balance to 5600k. So when the light passes in one angle thru alot of atmoshpere and out the other side to hit the moon, all the blue is gone.
edit: if we were on an alien planet with atmosphere of different molecular makeup the sky could be green
edit: if we were on an alien planet with atmosphere of different molecular makeup the sky could be green