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What would happen with this stack?:
Player 1 plays Banishing light targeting player 2's creature.
Player 2 plays Gods Willing on that same creature.
What happens with player 1's enchantment?
Does it do nothing because the target chosen is protected? Does it choose new target that doesn't have protection, since it isn't an enchant-aura? Or is it something else all together?
Part of what will help make this clear is that Banishing Light doesn't get targets chosen at casting time. Here's how Banishing Light normally plays out:
If you play Gods Willing to give a creature protection in between steps 1 and 2, no target's been chosen yet, and the player must choose any other target during step 3. If there are absolutely no other legal targets to choose during step 3, the triggered ability can't go on the stack, so nothing happens — we skip step 3 and 4, and Banishing Light now just sits there uselessly.
If you play Gods Willing to in between steps 3 and 4, you know what creature they're targeting with Banishing Light's triggered ability. If you give it protection, the ability can't resolve and will fizzle & be countered by virtue of having no legal targets left at resolution time. The player who controls Banishing Light doesn't get to pick any other creature; Banishing Light (again) just sits useless on the battlefield. Nothing gets exiled by it.
Assuming that Player 2 casts Gods Willing in response to Banishing Light's triggered ability, then the creature will be an invalid target for Banishing Light's triggered abilty, the triggered ability will be countered by the rules, and nothing will be exiled.
Here is what's going on in this interaction in detail:
Banishing Light's "When Banishing Light enters the battlefield..." ability is a triggered ability, as described in rule 603.1:
Triggered abilities have a trigger condition and an effect. They are written as “[When/Whenever/At] [trigger condition or event], [effect].”
This ability is put on the stack immediately after the Banishing Light spell resolves. It is at this time that the ability's controller chooses its targets. This is described in rules 603.3, 603.3d, and 601.2c:
603.3. Once an ability has triggered, its controller puts it on the stack as an object that’s not a card the next time a player would receive priority. See rule 116, “Timing and Priority.” The ability becomes the topmost object on the stack. [...]
603.3d The remainder of the process for putting a triggered ability on the stack is identical to the process for casting a spell listed in rules 601.2c–d. [...]
601.2c The player announces his or her choice of an appropriate player, object, or zone for each target the spell requires. [...]
After the ability is on the stack and the targets are chosen, player 2 casts Gods Willing targeting the same creature and choosing White. This grants Protection from White, which is defined in rule 702.16. In particular, rule 702.16b says
A permanent or player with protection can’t be targeted by spells with the stated quality and can’t be targeted by abilities from a source with the stated quality.
Then we can look at rule 112.7, which says
The source of an ability is the object that generated it. The source of an activated ability on the stack is the object whose ability was activated. The source of a triggered ability (other than a delayed triggered ability) on the stack, or one that has triggered and is waiting to be put on the stack, is the object whose ability triggered. To determine the source of a delayed triggered ability, see rules 603.7d–f.
Banishing Light is the source of the ability, and it is White, so the creature cannot be the target of the ability. Then, when the ability tries to resolve, rule 608.2b takes effect:
If the spell or ability specifies targets, it checks whether the targets are still legal. A target that’s no longer in the zone it was in when it was targeted is illegal. Other changes to the game state may cause a target to no longer be legal; for example, its characteristics may have changed or an effect may have changed the text of the spell. If the source of an ability has left the zone it was in, its last known information is used during this process. The spell or ability is countered if all its targets, for every instance of the word “target,” are now illegal. [...]
The creature that player 1 chose is no longer a legal target of the ability, and it is the only target that the ability has, so the ability is countered by this rule. Once that happens, Banishing Light simply does nothing. The ability doesn't trigger again, and player 1 has no opportunity to choose a new target.
