I doubt aviation GPS units cause problems with avionics. The best anyone has ever demonstrated with regards to RF interference is the CAA tests of mobiles when used in the cockpit. Away from the cockpit, i.e. in the cabin, the tests have been fairly inconsequential with those relatively high powered transmitting devices.
Meanwhile Lufthansa, for example, is happy (and with them, the FAA) to fit low power transmitting devices in the cabin, i.e. WiFi.
There's a huge amount of scaremongering on the subject of RF, but there's no analysis to give it weight. In fact, just the opposite. Most flights, like it or not, will operate with active mobile phones on board. Most GA flights, will run some kind of GPS. We are not in the midst of a zillion 737s or 172s crashing to the ground.
Nonetheless - leaving a mobile on, esp. if you are flight crew - is probably unwise, and for other unusual non transmitting gadgets the operator or commander's policy should be respected (i.e. Ask!) , if only to stop any in-flight issues caused by the percieved problem.