How much mains leakage does an Ethernet connection to a PC induce, and what is the operating leakage path?
The ethernet connection leakage current should be negligable, with UTP.
Every port has a array of transformers for high frequency, the leakage at 50 Hz common mode will be very low.


However, if shielded cable is used, S-UTP or CAT7 cables, there will also be made a chassis connection between the two devices.
Then the power supply leakage enters the equation, and those may leak several milliamperes. 

The simple act of reversing the plug might remove the nuisance tripping of the GFCI/RCD.

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