You could float the ground pin, then use a mA meter to measure the current going to ground.
IT equipment are FCC listed for both home and office(commercial) use, but that only covers EMF noise considerations. Computer equipment rooms are not GFCI'd and many IT support equipment are not designed to be used downstream of highly sensitive residential GFCI.
A UPS does lots of things that a GFI does not like -- as mentioned in posts above: bad power factor, leaky grounds, high inrush.
In the past, we have used "power conditions" to clean up nasty conditions like these. You want a passive "resonant" conditioner that is basically a giant coil (transformer) and capacitor that resonate at 60 Hz. You put this inline and it cleans up voltage/current phase shifts and sudden changes well. It is not a voltage regulator per se, and not a surge protector.
Or, try a different brand of GFCI. They all behave differently.