VFD amd GFCI do not seem compatible. I have a Jet 1221 VS speed lathe that will trip a GFCI as well as a larger Jet 1642 VFD lathe that will trip the GFCI outlets. So I have a single outlet in my shop that is just a regular duplex outlet with a regular breaker. All my othe outlets in my shop are GFCI protected.
The reason the GFCI gets trips is when a VFD changes frequency (voltage) it sends power back on the outlet. That is the exact thing that a GFCI looks for to prevent you from being shocked when there is a voltage differential between the ground and neutral.
So it is quite natural for a VFD t trip a GFCI. Some people do not have any problem with GFCI but I think most people will have the GFCI tripped by a VFD when it changes frequency to change the speed of the spindle.