A lot of VFD driven equipment work just fine on GFCI protected circuits, but some that does not. There is work going on in the appliance and equipment product standards as well as the GFCI product standard to address theses issues.
As far as the HVAC and GFCIs, some of that equipment won't work because the HVAC equipment used the EGC as a current carrying conductor.
In addition, there is nothing in the current product standard to address current to ground, whether it is by design or leakage, for that type of equipment. The assumption of the product standards has been that leakage current is not a real issue on hard wired equipment because it is much less likely that the EGC will be compromised on a hard wired equipment as compared to cord-and-plug-connected equipment. That is the very reason that all of the original GFCI requirements only applied to receptacles.
This will take time, as changing the product standard is done by the same type of process that is used to change the NEC and takes almost as long.
