The Hellfire Amulet introduced in patch 2.1 has a secondary affix that adds the effect a random passive ability for your class. If you do this on Monk and get Fleet Footed (Increase movement speed by 10%), will this increase movement speed if worn by another class?
No. While another class can wear any Hellfire Amulet, the passives themselves only activate when the correct class is wearing them. You can see this from the preview pictures of Hellfire Amulets on the PTR:
To be sure, some of the amulets don't have the (class only) text in them, but they will work the same. It's on the PTR, bugs are to be expected.