GFCI tripping is a known issue for the MP2 on North American power grids. I haven’t seen any mention of this issue on Quatros before but I would say it is highly likely. They are going to share a lot of the same internal components, which is where the problem is. North American GFCI outlets have a much narrower tolerance that European counterparts.
Most likely the reason we haven’t seen complaints about the Quatros and GFCI’s is because the overwhelming majority of mobile installations in NA have been MP. Mobile installations is going to be where you would usually see GFCI outlets being used to supply the inverter.
Edit: You are not the only one with this problem on a quatro: