On the space shuttle, the tiles on the back are in fact white to reflect away heat. The tiles on the bottom side however are black because black tiles are better at radiating away their heat. The side of the spacecraft facing the incoming atmosphere and the side facing away are both heated in entirely different ways.
I should add that the space shuttle is somewhat unique because its heat shielding was intended to be reusable. The bottom tiles protected the craft by being a very good thermal insulator. Most other reentry capsules have used an ablative heat shield. This style of heat shield is far more effective and easier to make, but it is burned away during reentry, meaning it’s single use only. It doesn’t matter so much what color an ablative heat shield is.
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