If a creature becomes the target of a spell that gives it protection, does that protection cause other auras to fall off?

When a creature gains protection from something (e.g., protection from white), the game immediately checks state-based actions. One of those checks is whether each Aura is still legally attached to its permanent (CR 704.5n). If an attached Aura now shares the protected quality — same color, type, or other characteristic covered by the protection — it is no longer a legal attachment and goes to its owner's graveyard.

Protection has four main effects remembered by the acronym DEBT: the permanent can't be Damaged by, Enchanted/Equipped by, Blocked by, or Targeted by anything with the protected quality (CR 702.16b). The 'Enchanted/Equipped' part is what causes existing Auras to fall off — protection prevents the creature from being enchanted by something it now has protection from.

State-based actions are checked continuously and don't use the stack (CR 704.3). So the moment the spell resolves and protection is granted, before any player gets priority, the game checks and removes any now-illegal Auras. They go to the graveyard without any player being able to respond.

Example: Your creature is enchanted with Pacifism (a white Aura). Your opponent casts Apostle's Blessing on it, giving it protection from white. When Apostle's Blessing resolves, state-based actions are checked: Pacifism is a white Aura now illegally attached, so it is immediately put into the graveyard. Your creature is now free of Pacifism.

Note that only Auras sharing the protected quality fall off. If the creature has multiple Auras of different colors or types, only the ones matching the protection are removed; the others remain legally attached.