It could be a N-E fault, and it is triggered by the compressor kicking in. So any large load would do the same as it causes enough of a volt drop on the neutral so sufficient current is diverted via the earth/CPC for the RCD to notice, and the fault may not be on the circuit you think is causing it if the RCD is also feeding a few other circuits.
If you have anything else with a large-ish motor that starts directly, say an old vacuum cleaner (not one with a soft-start electronic control) you could see if that does the same thing at that socket.
An electrician could run an IR test for such a fault, also they ought to be able to check for obvious faults on the appliance (the "PAT testing" sort of check). They also can test the RCD trip times and ramp-test to see what leakage current it actually trips at.
Replacing things "just in case" can be a more frustrating and expensive approach than methodical testing!