Does turning on inductive load (ex. AC motor) at peak input voltage reduce inrush current?
Is this true? Why?

The inductor formula is this: -
$$V = L\dfrac{di}{dt}$$
If the inductor is connected at the zero-crossing of the input voltage waveform, the &quot;natural&quot; rate of change of current is zero and, a zero rate of change of current only occurs at the peak of the inductor current (the peak of the current waveform). So doing this forces upon the inductor an unnatural situation and the peak current that is produced in the first cycle of AC will be about twice that taken when this unnatural situation has settled down. Of course, with core saturation, the peak current in this first cycle might be ten times more because you will drive the core into magnetic saturation.
This is why it is to be avoided.
Conversely, if voltage is applied at the peak of the voltage waveform the current rate of change is maximum but, (and very importantly) it's passing through 0 amps. This makes it a more natural point in time to connect the inductor to the supply voltage AND minimizes inrush current.
See the waveforms for both from here: -