There is no definitive answer to your question because there is no single cause of turn ON pops. Sometimes it's the switch that's responsible for the pop. Other times it's the LED. Sometimes it's the amp that causes the problem. It could even be a combination of any of the above. I have an AX84 High Octane tube amp that I built that is dead quiet with all my true bypass pedals. A few years ago I built a couple of different 18 watt amps (TMB, Lite, Lite II) and all my pedals that didn't pop with the HO popped with the 18 watt amps.
Thanks for the feedback - I have tried the unit with multiple guitars (active/passive/single or dual coil) and amps (all valve Fender pro/solid state Peavey) and in various signal chain configs ( or alone) there is no detectable change. The "pop" registers 68 dbA at 6 feet- in other words its significant. The Phase 90 is true bypass also and makes no noise. I will try a manual switch bypass - I have to say this is very disappointing as it renders the pedal un-useable. As an aside- I have a home-brew Germanium Fuzz that uses what appears to be the exact same switch (Mouser supplied) and is dead silent.
Lastly- I understand that turn on pops can be caused by DC offset or ground issues-but the turn OFF pop is just as loud.