What happens with two Pledges of Loyalty attached to the same creature?
For completeness' sake:


  303.4f. If an Aura is entering the battlefield under a player’s control by any means other than by resolving as an Aura spell, and the effect putting it onto the battlefield doesn’t specify the object or player the Aura will enchant, that player chooses what it will enchant as the Aura enters the battlefield. The player must choose a legal object or player according to the Aura’s enchant ability and any other applicable effects.


All cards returned by Second Sunrise are returned at the same time, so you can choose the Bears as the creature to attach them to for both Auras.
Right after it resolves, you will have a Grizzly Bears enchanted with both Pledges, two instances of Protection from White (and Green) that each don't remove the Aura that grants it.

Now, State-Based Actions are checked - simultaneously for each card, as per the following rule:


  704.3. (...) the game checks for any of the listed conditions for state-based actions, then performs all applicable state-based actions simultaneously as a single event. (...)


Since both Auras are illegal at this time, they will both be put in your graveyard as a State-Based Action, even though a single one of them could remain on the creature (which SBAs don't check for).


  704.5n. If an Aura is attached to an illegal object or player (...), that Aura is put into its owner’s graveyard.