Well first you need to know how a GFCI works... Imagine a teeter totter. There are two children both exactly the same weight sitting very still and the beam is balanced... Now hand one of them a glass of water (8 oz) and that end quickly hits the ground.
The children are the BLACK and WHITE wires in your power system.. And when one of them carries even a tiny amount more current than the other.. The thing trips.
Now. The converter.. There are two types and yes Some of them DO not play nice with GFCI devices.
one is a transformer supply.. In theory these should work since in a true transformer there is no common connection between the 120 volt and 12 volt side.. However I suspect some might use an autotransformer (Single winding tapped at the proper point for 12 volts, which by the way is about 8-9 volts AC)
Others are "Switching Supplies" and frankly.. I'm not comfortable describing them but it is possible they may "Unbalance" that teeter totter.
Reports are that some converters will only do it if the batteries are low
Others only do it if the batteries are full
Others do it all the time
And still others never do it.
Alas that's all I can tell you.
