Put in the GFCI.
Don't believe the old wives tale that motors cause GFCIs to nuisance trip.
GFCIs are designed to work with motors otherwise every hand tool, pond pump and spa would experience nuisance problems. IMO, cheap motors use cheap capacitors which leak to their case. This leakage causes ground faults which in turn cause the GFCI to operate as intended.
If you experience trips with GFCIs fix the load, don't blame the protective device.
