An interesting read on what conditions can cause nuisance tripping.
Unfortunately it does not say anything about why. It is a subjective warning about what may and may not work. And that, unfortunately, is vague, subjective reasoning that does not say why with numbers.
Those GFCI testers can only report some defects; can never say anything is good.
A sump pump can be leaking 4 milliamps constantly - and not trip a GFCI. One connects another appliance which causes a GFCI trip. Subjective reasoning (also called junk science) then blames the other appliance.
Meanwhile I built a tester than intentionally created an adjustable leakage current. So that I can measure how much leakage causes a GFCI to trip. Good GFCI trips at between 4 to 6 milliamps. If it trips lower, then we know some other appliance has a human safety threat. So it may cause 'nuisance tripping'.
All honest discussions define everything quantitatively. That means numbers are always included. No numbers is a first indication that it might be a scam.
Second, a transmitter should not create a 5 milliamp current on AC wires. GFCIs work just fine in the massive E-M fields even in transmitter facilities. However it can induce micro-amp currents. That combined with leakage elsewhere could result in 'nuisance tripping'. Solution- find and fix that unacceptable other leakage. Never foolishly make a conclusion from myths that blame 'nuisance tripping'.
One always learns what is defective long before making accusations or a conclusion. Classic junk science is to see a GFCI trip. Then wildly speculate it was caused by some other (perfectly safe) appliance or a radio transmitter.
That sump pump apparently has a human safety defect. So someone with contempt for human life used a classic urban myth (nuisance tripping) to justify removing a GFCI. Used a conclusion only from wild speculation to endanger human life.
Long before making such conclusions, the informed first learn the whys with numbers. One who cannot must find someone to teach or somehow to learn basic electrical concepts before making a conclusion. 'Nuisance tripping' is an 'easy to promote' urban myth.