Hi, did you ever solve this issue?
I have the exact same issue with my bluetti AC200. If I plug my Dometic CRX50 12v fridge into the cigarette port (and have tried the 25amp aviation socket too) with nothing else using power the fridge lights come on but the compressor fails to start, and the red error light flashes once, indicating low voltage.
I've checked the voltage on the cables and its 13.4v.
If I then add 10-15w of drain to the dc outputs by turning on some lights for instance, the fridge compressor starts perfectly and no error lights show.
I've even tried plugging the same cable into my AC50S and the fridge runs fine off that (with nothing else powered by the AC50S).
I'm sure when I first got the AC200 several months ago this wasn't an issue, but I suspect that back then I had a couple of 12v parasitic drains in my system (usb socket always powered on, diesel heater display powered on etc) - I've since put switches on all of them to try to conserve power.
Thanks