For the white moon, it represents the first goddess (Lucifer), of the first quarter of the cycle. Since it is normally covered, either with a yellow (solar color, gold color). White, a symbol of light, but also of purity. Whereas the red moon is the moon, covered with the blood of her son (she absorbs her son). Or the blood, which is associated with tears, covers the mother. The light returning to her, disappears.
In the 'Lord of the Rings' series, Legolas announces that the night has been bathed in blood after seeing the red moon.