Yeah, what brand? Engel provides a chassis ground screw just for this reason. At a high level Engel's swing motor works on AC and there's a DC-fed inverter that drives it. There are then two supplies that provide DC to this motor driver, one a fairly simple AC/DC supply when on shore power and another DC/DC supply for 12V. They do this because the motor runs at 27V IIRC, so they have to boost the 12V.
It might seem odd, but they are usually quite a bit more noisy when used on battery than on the mains. So Engel built the case so the inverter and supplies live inside a shielded enclosure. If the fridge case itself is left floating or has a poor ground connection, the thing will be a huge RFI source. It's pretty important to do this if you run HF, there are three switching supplies in your fridge that will swamp your RX.
If you don't have an Engel it might not be exactly the same situation, but for Engel and ARB fridges a good test is to run the fridge on AC and see if the noise abates or changes, then you know it's just a matter of grounding the case. If this does not help, then you have to get more aggressive with chokes and bypassing. The majority of the noise should be fixed just grounding the case, though.
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"To live is to suffer, to survive is to find some meaning in the suffering." -- Friedrich Nietzsche