Her being a mage WOULD take away a lot of what the Chantry teaches on mages. That they must be controlled, that they MUST be in a Circle, that without the Circle they will inevitably become malifacarum, and that mages are responsible for the Blights.
If she was a mage, the rhetoric used against free mages causing blights and using blood magic will be a lot weaker because Andraste was a slave, never went to a circle, and so on.
She was the chosen of the Maker, a Prophet and closest to the God the majority of Thedas buys into.
Beyond that, she existed before those institutions did, Beyond that, Magic is already seen as a gift by the Maker if one that is often abused.
It would also be a huge threat to the stories of the miracles she supposedly performed with the makers aid. It would cause questions, like did she really cause a draught or did she use fire spells to burn crops? Did she really meditate for days or did she walk in the Fade as a Somniari? These questions would lead to people questioning her divinity. And to do so would undermine the authority that the Chantry has when they act in both her's and the Maker's name.
Her being a mage would be an almost direct threat to the Chantry and their doctrine.
Whom is to say physical manifestation are not will of the Divine, It goes into a matter of faith that, i don't see how it would be anymore different from what happens already with the religion of Andraste. Beyond that, She is not divine, she was the chosen of the Maker, She could call upon his grace, but none of the power was hers, She was only revered that highly by the Disciples of Andraste, whom forsook the Maker in favor of a High Dragon whom they gave a pet name.
Beyond that, How is it undermining Chantry authority, if anything it proves that the only true good intentioned mage who could manage their power has long since been gone from the world.
I really don't see it that way obviously.