The attribution of compassion to Xthonos. Xthonos is the unmoved mover, unaware of anything but Its own perfection. Anything that compromises Its transcendence, any doctrine that implies Xthonos cares about creation, is heresy.
Ecclesiasts do have sweeping powers in situations of heresy. In practice, those can be limited by a strong aristarch or Alastor captain, who could arrange for an over-the-top witch hunter to be replaced for excessive disturbance to the local order. But in this case, Aristarch Stilos was the one who reported the heresy to the Archimandrite and asked him to send a proper inquisitor to sort things out. The young noblewoman's execution would have been with his approval.
In the alternate universe of the Plektoi intro, Stilos is annoyed at Zebed for calling in the hounds (mentioned in the third option I added there), which he thinks excessive. In the Olynna intro, they're of one mind on the danger of a heresy promulgated by the current Ecclesiast, and the necessity of a strong response.