GFCI keeps tripping. Why??

I have a (new to me) small Class 'C' Chateau Citation. The Norcold Model N611LT trips the GFCI every time I plug it into 120V. The fridge works fine when I bypass the electrical receptacle behind it and the GFCI does not trip until I plug the fridge in. It works fine on propane. I've replaced the GFCI and the new one also trips. Spent a couple of hours on it this afternoon and I'm stumped. I'm going to put in a regular receptacle for now since I'm going camping to-morrow morning.. but there has got to be a reason it is doing this. Anyone have an idea what could be causing this?? I won't have wi-fi once I leave to-morrow but I'll only be gone a week and it would be nice to get this resolved. I don't like the idea of having receptacles with no GFCI provisions :(