Attached photo of the connections on an Engel MT45, the chassis ground is in the lower right. I suspect most fridges will have this. If not, screwing a ground strap to the case, maybe under a bolt or something, would achieve the same thing. Although it's not necessarily going to be the case that all manufacturers take the time to design their cases for RFI. I wouldn't be surprised to hear Engel actually tests their fridges for EMI/EMC.
The noise is unlikely to be strong enough to cause any damage unless /maybe/ you touched the antenna to the noise source. It just takes inches in air to attenuate the noise from damaging to irritating. Or at least the signal strength goes down enough that your radio AGC can deal with it to protect itself. I should clarify, this is the case with noise generated from a fridge or computer or whatever, which is relatively low power. You would not want to hold your HT inches from a 50W mobile antenna while it's transmitting, that would likely ruin your HT.
The problem really with RFI like this is that a strong local noise source will desensitize your radio's RX. When you squelch out the noise or gain is reduced it will take a very strong signal from other radio operators before you hear anything. So a fridge 10 feet away might generate the same local signal strength as a regular station 25 miles away, for example.
"Stand your ground. Don't fire unless fired upon, but if they mean to have a war, let it begin here." -- Capt. John Parker