I'm against nylon washers, but only theoretically. The same properties that cause an easy turn of the tension rod will also allow the rods to more easily go out of tune. A steel washer creates more friction, and will hold a tuning better. In reality, the nylon washer may still cause enough friction under tension to hold the rod secure, but I've heard stories from heavy hitters (which I am not) that the nylon washers do not work for them.
This raises the question of : why do drums go out of tune? do they go out of tune because plastic stretches , shrinks and expands with temperature changes and the aluminum hoop expands and contracts with temperature changes; the shell deforms temporarily due to tension, expands and contracts with humidity and temperature changes( if wood) and many hoops give slowly under tension or is it because the tension rods vibrate loose over time?
I'm not so sure that back slippage against the washers is a huge factor but I do think that nylon compresses, while steel, stainless steel and brass do not----under the pressure encountered beneath a tension rod.
If you use skin heads ,you have a whole other problem related to humidity but less of a problem than plastic related to temperature.