While running the Wrath Within mission on the villain side (USPS), when you have to use the machine to turn into a Wrath demon, if you have a pet up it says "resist" and doesn't work. Instead you have to manually banish the pet to continue the mission. So far, I've only tried with Brick and Crystal, but I would think this goes for Fury, Guardian, Watcher, and Suppression Turret.