Nothing about taking control of an opponent's equipment makes it fall off. An equipment you control CAN be attached to a creature you do not control. The equip ability cannot target such a creature, but attachment by other means or circumstances, like in this case, is not prohibited. The equipment was under your control, and it was still legally attached to your opponent's creature. You have to move it to one of your creatures, usually by using its equip ability, to unattach it from that creature. Or if it is a reconfigure card, pay the reconfigure cost to turn it back into a creature.

In the case of Dragonfire Blade, the equipment grants the equipped creature the stated abilities. So that creature still had hexproof from monocolored, and as the opponent of that creature's controller, you could not target it with monocolored things.