Interesting. I had the opposite issue - GFI kept tripping whenever I tried to charge the car. Had to run an extension cord into an adjacent room with a regular plug (non-GFI) until I rigged up a 240v charging solution off the dryer outlet.I should clarify that the 110V outlet that we use for the yellow cable had to be specially installed in the garage because all the existing outlets were GFI which the Roadster didn't like ("extension cord detected").
When we upgraded our electric service last December (before the credit ran out), I added a pair of 20 amp GFI plugs along with the 14-50 outlet that I now use. Given the overall cost of the upgrade, they were essentially free. I tried the 120 volt yellow cord on the new GFI outlets, and it worked (no trips)! So, it appears that the GFI on the original garage plug is either faulty or overly sensitive. The Roadster 2.x is known to be a little more "leaky" in its grounding, but given that my ham radio can sometimes trip the same GFI outlet (even though not connected through it), and seeing that the new outlets work, I'm inclined to believe the old outlet is the problem, not so much the car. Or, did the standard for GFI tripping change in the last, um, 35 years since the house was built?