Pete C. wrote:
Motors and solenoid valves are the least likely components to care
about the AC waveform. Both motors and solenoid valves are routinely
operated with PWM type drivers which produce waveforms much further
from a sine wave than a "MSW" stepped square wave inverter.

Routinely? On a simple furnace that's 25 years old? Rest assured the
motors run directly on line power and the electronics such as there are on
24 V from a transformer.

As long as the inverter is appropriately sized it should be fine.

2500 continuous, 5kW surge.