Power supplies for electronic devices operate by rectifying the incoming AC and charging a capacitor to peak. The energy in this capacitor then operates the switching supply. If the peak of the incoming AC is clipped this critical raw voltage will be low and the power supply, depending on its tolerance for this condition, may not operate properly.
The magnetron may depend on a sinusoidal waveform, shaped by a network in the high voltage circuit, to kick it into oscillation. A magnetron is a vaccum diode with a magnet that causes the electron beam to curve past resonant cavities in the anode, these cavities oscillate and bunch the electrons and that amplifies the oscillation. Too high a voltage caused by a square wave would cause electrons to hit the anode early, too low and they may pass to far from the first cavity.