It hit me why I hate the Exarchate so much while excusing Zhuchka for similar things. It's because they are actively hostile to the core of the mythos in a way that she isn't. Zhuchka still has own philosophy, a series of beliefs that were created from the events of her life before she met her false god. The Heterodoxy just completely delegates their Meaning to the Outsider System. Not the gods, or even a particular Outsider because that would allow the will of somebody, something actually able to write Meaning into the world, to override the next whim of the gods' soul gacha. They're even better at denying Meaning than the Ecumene, whose nihilistic mission is at least filtered through a living person instead of the God-Script equivalent of 1s and 0s, and this superiority at least had the mercy of making them relatively impotent compared to their later imitators.
It's the total opposite of the Second Seat. The Second Seat believes that the gods' ideals are more important than their personalities. The Exarchate, not just the Whites but in fact anybody who preserves their system of government, reveres the gods without understanding their goals and mission at all.