I have a similar problem. I noted that when the light bulb on the fan
fixture is illuminated the problem does not occur. Perhaps a
resistive load across the fan absorbs any power line spikes which
trip the GFCI. Just an idea.

In my case, the fan is just a fan. No light or heater in it.

Wiring is about as simple as it gets. A single incoming 12/2 cable coming
from the switch. Fan housing is grounded, hot and neutral are connected
according to the fan instructions (black to black, white to white. No
brainer).

Anthony