The chaotic nature of the ML faction is due to the fact that there's no tangible hierarchy beyond the Vicar's word being mostly listened to, and the least amount of organization between the other churches. The Church in Vallaki can do what they want and the Churches in other places won't say much.
Though we see this Chaotic alignment falling everytime a DM NPC speaks, the High Priest doing a proclamation, or Ilie, or Lizuca and so on. It is loosely supported, it just shows itself in things like;
Anyone can do sermons in the clergy, and no one will slap them and be like "NO YOU CANNOT BECAUSE YOU ARE NOT VICAR" or whatever. There are no 'specific' orders Lightcarriers of Dawnbringers need to listen to beyond "keep the peace, be nice, have common sense and praise the Morninglord" after initiation.
..this doesn't mean they will allow people to summon whatever in the Church, run around with weapons, cast all sorts of magic- nah. The Chaotic alignment of the faction is more internal than external. I could go on and on about this but..
I am in favor of this change.