Does Animate Dead's trigger cause the aura to fall off if the creature it enchants has protection from black?

Animate Dead is a black Aura enchantment. Protection from black means the protected creature cannot be enchanted by black permanents (the 'E' in DEBT: Damaged, Enchanted/Equipped, Blocked, Targeted by black sources). This is governed by CR 702.16e, which states that protection prevents the object from being enchanted by sources with the specified quality.

State-based actions are checked continuously. CR 704.5n specifies that if an Aura is attached to an object it cannot legally enchant, the Aura is put into its owner's graveyard. Because Animate Dead is black, it cannot legally enchant a creature with protection from black, so 704.5n causes it to detach and go to the graveyard.

When Animate Dead leaves the battlefield, its 'leaves the battlefield' triggered ability fires, requiring the creature to be sacrificed (or returned to the graveyard, depending on card version). So yes — the protection causes the Aura to fall off, and that departure then triggers Animate Dead's leave trigger, usually killing the creature.

Example: You use Animate Dead to reanimate a creature. An opponent's effect gives that creature protection from black (e.g., via an instant). State-based actions are checked: Animate Dead is black and now illegally attached, so it goes to the graveyard per CR 704.5n. Its leaves-the-battlefield ability triggers, and the reanimated creature must be sacrificed (or returned to exile/graveyard per the card's text).

Note: Protection must be present after Animate Dead has already resolved and attached. If the creature had protection from black when Animate Dead tried to target it, it couldn't have been targeted in the first place (CR 702.16b). This question applies to protection granted after Animate Dead has already resolved.