Given the numbers who were on the same side as his right-hand man and son (both of whom give the impression of being more rigorist than Geofram), it seems likely that a majority of the Children share his opinion.

Also it's hard to call Asunawa an abberation when he's risen to the 2nd most powerful position among the Children. A person doesn't raise that high in an organization like that unless those above them approve of his methods.

And you say this in criticism of an organization whose arch-enemies had TWO Darkfriend Keepers at once? You also exaggerate Asunawa's influence within the CotL. He was the number two man in Valda's administration, because of their alliance in pulling down Niall, but in normal times, he's no more than their equivalent of a single Sitter or Ajah head. He was merely the leader of one faction, and condemning the Children for having such a faction is like condemning Andor for having a Lord Elegar or Lady Arymilla, Cairhien for having a Colavaere or Toram, or the Tower for having an Elaida (or an Egwene).