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My half-elf storm herald barbarian, Finn Wardell!!
If I play a Storm Herald and get back Imprisoned in the Moon and something that grants protection from blue (lets say Blue Ward), which falls off first? Does not being a creature mean the creature aura falls off, or does protection from blue mean the blue aura falls off?
They both fall off at the same time.
When state-based actions are checked, everything that needs to be done by them is noted and then all of those things happen simultaneously. No state-based action takes priority over any other.
In the example you cite, Imprisoned in the Moon is illegally attached to Storm Herald because Blue Ward is giving Storm Herald protection from blue while Blue Ward is illegally attached because Imprisoned in the Moon makes Storm Herald no longer a creature. An illegally attached aura goes to its owner's graveyard when state-based actions occur, and so both Auras would be put into your graveyard. However, Storm Herald's replacement effect causes them to be exiled instead.
Storm Herald
Artist: Aleksi Briclot TCG Player Link Scryfall Link EDHREC Link
Storm Herald
Artist: Aleksi Briclot TCG Player Link Scryfall Link EDHREC Link
STORM HERALD ANDRI TIME!
Today we have Prax, the Tabaxi Storm Herald Barbarian.