Does a creature with protection from white get destroyed by a white board wipe like Wrath of God?

Protection from a color grants four specific shields, remembered by the acronym DEBT: the creature cannot be Damaged, Enchanted/Equipped, Blocked, or Targeted by sources of that color (CR 702.16b). Notice that 'destroyed' is not one of those four protections on its own.

Wrath of God (and similar board wipes) destroys all creatures without targeting any of them. Because the spell doesn't target the protected creature, the 'T' shield from protection does not apply. The creature is simply included in the mass destruction effect as a non-targeted object (CR 114.9, 702.16b).

Additionally, Wrath of God's destruction effect is not 'damage,' so the 'D' shield doesn't help either. The creature is destroyed just like every other creature on the battlefield.

Concrete example: You control a White Knight (protection from black). Your opponent controls a Knight of Infamy (protection from white) and casts Wrath of God. Both knights are destroyed, because Wrath of God targets neither of them — protection is irrelevant here.

The only way a white creature could survive a non-targeted board wipe is through a different ability, such as indestructible (CR 702.12), not through protection from white.