I may have been the poster with the Norcold 704DE from a boat.
That was a swing compressor, which does not exhibit the starting surge than rotary compressors do.
The swing compressor is a solenoid that is driven back and forth by the alternating current and the first cycles if the solenoid doesn't make a full stroke it doesn't care.
A rotary compressor must make that full stroke plus the surge of the motor starting so it needs a lot more current capability to get it running.
I doubt that the fridge motor cares if it is a sine wave or not. Sensitive electronics don't like the square wave due to the spiked associated with them.
I tried a dorm type of fridge before I got the Norcold unit, but my 300 watt inverter would not start it, but fault out when the motor tried to start. Not a problem with the non-pure sine wave, but rather the high starting current typical of this type of thing. You may need a MUCH larger inverter to take care of the surge. 300 watts won't handle starting a 50 watt motor in a dorm fridge.
Some people have had a problem with them with a 1000 watt inverter. The starting current is immediate and large and the inverter senses it immediately and faults.
However since the fridge is just a motor and thermostat I doubt that the modified sine wave would damage it, but to each his own.
The same 300 watt inverter will happily run the Norcold 704DE in 120 volt mode if that counts for anything.
By the way I am a beginner with electrical
things only having worked with that stuff for 50 years or so.