Yes, it does. Protection from [blue] does 4 precise things and nothing else. You can use the word DEBT as a mnemonic trick:
Prevents Damage from [blue] sources
Can't be Enchanted or Equipped by [blue] auras and equipment
Can't be Blocked by [blue] creatures
Can't be the Target of [blue] spells or abilities
Exhaustion doesn't damage, enchant or equip, block, or target, so it works fine on things with protection from blue.
I'm a former judge (lapsed), who keeps up to date on rules and policy. Keep in mind that judges' answers aren't necessarily more valid than those of people who aren't judges; what matters is we can quote the rules to back up our answers. When in doubt, ask for such quotes.
Prevents Damage from [blue] sources
Can't be Enchanted or Equipped by [blue] auras and equipment
Can't be Blocked by [blue] creatures
Can't be the Target of [blue] spells or abilities
Exhaustion doesn't damage, enchant or equip, block, or target, so it works fine on things with protection from blue.