My GFCI trips when the surge protector is plugged in

All surge protectors leak a small amount of current to ground. A GFCI is designed to trip on exactly that, so this is expected.

Plug into a circuit that isn’t GFCI-protected. Campground 30A and 50A pedestals shouldn’t be GFCI. This usually happens at home, on a garage outlet, while the RV is in storage.