Meaning of "the body soon learns to stand down in the face of fat"

In this case it's the second meaning of "stand down." Since the body is used to olestra, it thinks that real fats are not actually fats, and it won't attempt to break them down, going "off-duty." This leads to fat accumulating.

It's a terrible mixed metaphor. As Jackgill points out, it's the second meaning is closest. I think of "stand down" as chiefly military, meaning to abandon an aggressive position. There's even a charity for drug-addicted homeless veterans called Stand Down.

"In the face of" is phrase referring to the imminence of some negative condition. Military law says "in the face of the enemy"; you might also hear "in the face of disaster" or "in the face of defeat".

Putting an vague expression together with an anthropomorphizing metaphorical phrase and you get, as you have seen, confusion.