If the socket (like in the kitchen, batheoom, etc.) requires a GFI, do not change it, just do not try to use it for EVSE charging.
Since many GFIs are too sensitive to work reliably with an EVSE, try to use a NON-GFI socket with the EVSE (of course also properly Grounded), a 3-prong (5-15 or 5-20) socket.
In short, do NOT use a GFI socket.
It is OK to try a GFI socket, and OK to use it IF it works with your EVSE and car, but just realize that it MIGHT not work reliably (as you experienced).