It is especially troublesome that the GFCI trips only when the laptop is
plugged into the power supply. There is supposed to be substantial
electrical isolation between the so-called "hot" and "cold" grounds
(i.e., between the AC and DC grounds). Unless that isolation (usually an
opto-isolator) is compromised, I can't imagine a mechanism by which the
laptop itself could trip a GFCI, even if it were hanging overboard and
immersed in seawater while connected! Not so for the power supply, of
course.

Larry's theory of a monster-sized common-mode switching noise signal
propagating through the AC lines to trip both GFCI outlets is looking
more attractive. At least that theory supports a mechanism by which
plugging in the laptop causes a GFCI trip: going from no-load to
full-load would cause a change in switching characteristics that might
produce more noise on the line.

20,000 ohms or less of leakage can easily be measured on a DMM and
leaking RF filter capacitors are common. It would be a good idea to
measure leakage with and without the laptop connected to the power supply.

Chuck

w_tom wrote:
All appliances have leakage. Leakage that should be so low
as to not add up to a problem. It is doubtful that laptop is
leaking milliamps on startup. IOW there would be something
else on the circuit leaking so much that just a little laptop
leakage could trip the GFCI.

Unlikely that you will find leakage with the ohm meter.
Try. But eliminating other items from the circuit, then
powering on the laptop will probably provide better
information.

Informative may be a current measurement of that circuit's
ground wire. How much current (in AC milliamps and DC
milliamps) is flowing down that ground wire for various
powered on appliances on that circuit?