because I assume you're using an isolating transformer so you can work on something live a bit more safely. If the appliance has components (eg capacitors, especially vintage ones, or a leaky mains transformer) connected between its earth conductor and its live or neutral, and you connect its earth to mains earth, then you are connecting components between the 'isolated' side and the mains earth, so the item under test is no longer completely isolated from the mains earth. Touching the supposedly isolated live or neutral may use you and a faulty component to complete the circuit. You may therefore be under a false sense of security.
If its a 2-wire only appliance eg live chassis radio then the output socket earth wont be connected. But if its an appliance that needs an earth under normal conditions, then leakage to earth may manifest as an earth-referenced live or neutral.
When I worked for another company our isolation transformer had a sense relay that cut the power if it saw any voltage coming back on the appliance earth conductor, like a voltage-operated ELCB.
I think
