What the wider world remembers of the war and the fragmenting has been distorted over the long span of time since it happened.
Original truth (lost to most): Those who could shift into many forms were targeted and killed by the divines (or their agents) in the aftermath of the war. The instruction passed down through survivors was practical and urgent: hide what you are, or you will be killed for it.
Current belief (what people actually think today): Over generations, that warning twisted into something closer to institutional doctrine: the congregation (organized religion, i.e. the High Church) will hunt you, because the ability itself is seen as a corrupted, twisted version of the Lunar Mother's power.
The fear is the same shape. The reasoning behind it has been completely inverted — from "hide from those who fear true power" to "hide because what you are is itself wrong." Most people, including likely most of the High Church itself, do not know they are enforcing the echo of an ancient war rather than upholding a moral truth.