This is not an uncommon anomaly. As others have said, the NEC doesn't
require GFCI protection for the fan unless it's located over the tub,
and the manufacturer requires it

Well, good to know, but a little too late. It had been my understanding
that the entire bathroom circuit needed to be protected by the GFCI. But
the inspector mentioned a couple of things that didn't need to be on it
also. Oh well, no harm done, except for the fan nuisance.

The DPST switch idea sounds like my best option if I can find one.

Anthony