No-one has spelled it out, yet (perhaps it's obvious to all reading, here?) but remember that the output of a variac is REFERRENCED TO THE MAINS NEUTRAL SIDE and NOT ISOLATED! Worse still; wire the variac primary into the main power supply incorrectly, and the entire output will be referrenced to Mains Live! ZZZT....
Also many units - even quality ones - may be supplied as "open frame" - that is, not contained in a safe end-user case, but designed to be built into an equipment cabinet of some kind.