A physicist would tell you something else though: The reason is the sunlight that passes by the earth closely while still traversing the earth’s atmosphere. While traversing the atmosphere the white sunlight gets scattered (scattering shouldn’t be mistaken with refraction). From the whole spectrum of colors inside the white sunlight it’s the shorter wavelengths (like blue) that get scattered most. This leaves mostly the red light passing fully through the atmosphere. Also due to the scattering the light changes its direction slightly and shines into the earth’s shadow where it hits the moon.

Basically the moon goes red for the very same reason that the heaven appears red during sunset.