Does an aura attached to a creature fall off if the creature gains protection from its color?

Protection from a color means the protected permanent cannot be 'enchanted' by sources of that color (among other things). This is encoded in CR 702.16b, which lists the four effects of protection using the mnemonic DEBT: the permanent can't be Damaged, Enchanted/Equipped, Blocked, or Targeted by sources with the specified quality.

When a creature gains protection, the game immediately checks whether all permanents on the battlefield are in legal states. This happens via the 'state-based actions' rules (CR 704.5n), which specifically state: if an Aura is attached to an object or player it can't legally enchant, it's put into its owner's graveyard. Protection makes the Aura an illegal enchantment, so state-based actions move it to the graveyard.

This happens without using the stack — no player can respond to the Aura falling off. It simply ceases to be attached as soon as state-based actions are checked after the protection effect resolves.

Concrete example: Your opponent's Grizzly Bears is enchanted with Unholy Strength (a black Aura). You cast Apostle's Blessing and give the Bears protection from black. As soon as Apostle's Blessing resolves, state-based actions are checked: Unholy Strength is a black Aura illegally attached to the Bears, so it's immediately put into the graveyard. The Bears loses its +2/+1 bonus.

Note that if the creature later loses protection, the Aura does not automatically re-attach — it stays in the graveyard. The effect only causes the Aura to fall off; it doesn't create any further interaction after the fact.