The fridge shouldn't be on GFCI in the first place
GFCI is designed to protect humans from
- typically 2-prong ungrounded,
- appliances where the electrical parts are anywhere near a place you can reach
- where the appliance may get wet, including its electrical bits
- where it, or you holding it, could get into water e.g. Sink
- and where all this couls possibly add up to an electric shock
A refrigerator is none of these. It's a grounded all metal chassis that can't move, all the electrical gear is all in the very back at the bottom where you could not possibly reach it, it won't get wet and you won't drop it in the sink.
Compare to the Range, which definitely has no GFCI protection, and is probably even wired NEMA 10 with no ground at all, and with the range chassis bootlegged to Neutral, seriously? how can this be legal?
And in fact, there is no Code requirement whatsoever for GFCIs on fridges.
Use a non-GFCI supply, preferably a dedicated circuit
The fridge is probably tripping because it does have a ground fault. You can armwave, and call it some oh/so/complicated motor issue, but it sounds like semantics to me, at the end of the day currents are not equal. The motor isn't storing quintillions of electrons, heck the new cyclotron at Berkeley Lab couldn't store that many electrons. The electrons are being returned in real time, and we know it's via ground because that is the only reliable return. That's a ground fault by definition. Whatevs. The point is that for all the above list of reasons, we don't care that much if a fridge has a small ground fault.
It's not safer; "everything's safer with GFCI" is simply not true, again for the above bulleted reasons the fridge is vanishingly unlikely to bite you. You have more to fear from that NEMA 10 range. Seriously.
If able, give the fridge a dedicated circuit with a special 1-socket receptacle that plugs in behind the fridge, and don't look back. Otherwise rearrange so the fridge is non-GFCI, but you still have a risk since sharing a circuit still invites an overload trip causing food spoilage.
Food spoilage is dangerous too - you imagine that "oh, the chef will taste the food first" no. Food for children or senior citizens is typically served blind. I have watched aides serve my mother a bowl of cereal with curdled, way out of date milk. Again, you have to balance other safety factors with the "everything's safer with GFCI".