I had perhaps the same problem (perhaps not).
My AC and furnace would run at the same time. Turns out my thermostat had a "differential" setting. D1/D2/D3. It was defaulted to D1. When set to D3 the problem went away.
I supposed it was that the thermostat was no longer looking for set temperatures so close to the actual temperature that it thought the RV needed heat and cooling.
I forget exactly how I change to D3. Something like pressing "up temp" and power at the same time.
See https://www.forestriverinc.com/brochures/0000/0000ThermostatSingleDometicManual.pdf