Earth removes the blue light first
During a total lunar eclipse, Earth blocks the direct sunlight that normally illuminates the Moon. Yet Earth’s shadow is not completely black. A thin ring of atmosphere surrounds the planet, and sunlight passing through it is filtered and bent.
Molecules and tiny particles scatter shorter wavelengths of visible light, especially blue and violet, more strongly than longer red wavelengths. This is the same broad reason a clear daytime sky looks blue and a low sunset can look orange or red. After the bluer light has been scattered away from the direct path, the remaining warmer light is refracted into Earth’s umbral shadow and reaches the Moon.
Why the shade changes from eclipse to eclipse
There is no single official “blood moon red.” A total eclipse can look bright copper, burnt orange, brick red, brown, or unusually dark. The color depends partly on how deeply the Moon enters the umbra. It also records the state of Earth’s atmosphere along the ring of sunrise and sunset locations filtering the light.
Large volcanic eruptions and widespread smoke can load the atmosphere with particles and make an eclipse darker. Clearer atmospheric conditions may produce a brighter orange Moon. Local haze in front of the observer can add another layer of color, especially when the eclipsed Moon is low.
A useful way to picture it
If you could stand on the Moon during totality and look back toward Earth, the planet would cover the Sun. Around Earth’s dark disk you would see a glowing reddish ring made from all the sunrises and sunsets happening at that moment. That ring is the light illuminating the lunar landscape.