Your faction with many NPC groups is modified by your choice or race and religion. When an enchanter uses an illusion spell, he temporarily replaces his racial faction modifier with that of the race he is illusioned as. However, his religion based faction modifier is still present. If a certain group is sufficiently biased against a certain religion, say High Elves vs Innoruuk, then your illusion might not be enough to bring you out of KOS status, or at least, not bring you all the way to indifferent, you might still be dubious or apprehensive, which might prevent you from doing a quest turn in, or buying/selling at a merchant. If an enchanter is agnostic, he can become indifferent in any city with the appropriate illusion spell.
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