How come we can put aluminum foil in the oven but not microwave

In a microwave, foil, especially crinkled up foil, messes up the electric fields produced by the short wavelength radiation. High currents can flow in the foil even to the point where it catches fire. It also reflects a lot of the energy so food wrapped in foil doesn't get hot.

Infrared radiation in a conventional oven doesn't care one way or another about foil. Well, ok, it reflects some, but nothing interesting happens.