Really, saying the hat is armored, or is laced with it on the inside of the hat has it make sense mechanically and IC. Just have any helmet you have stand in for the hat's AP.
People are referencing the models too much and as i said in my previous post GW designs the models to look cool and sell, not be realistic interpretations of how that unit would actually be kitted out - space marines would be bedecked in grenade belts, clips of ammunition, armour sealant sprays, combat blades, shields and any other number of devices that they use in the fluff but arent on the models.
A priest is only nominally attached to a guard unit, often by their own choosing and so they can go into war equipped however they wish - im sure some come with gilded carapace armour and golden robes!
Commisars similarly may have their distinct dress uniforms while the regiment they are attached to is billeted but when they get assigned to a combat zone im sure nobody would begrudge a commisar demanding a suit of flak or providing something better themselves.
"Only the insane have the strength enough to prosper. Only those who prosper may truly judge what is sane."