Oh, so they're basically just anarcho-primitivists!
Jokes aside, thanks, you two, I think I get it now. I almost got confused again when I read the White Wolf Wiki entry for the Via Apep, which says "This view is anathema to
Setites on the
Road of Set, as Set himself hates chaos and its manifestations", but I think I got the distinction down now.
Materially, they're all doing the same, but the reasoning and theological system is slightly different.
The Road of Set is the heavily Gnostic version. Ra is their Demiurge and Set their Monad. They do not worship chaos or corruption, it's just a means to an end. Once the material world has been fully destabilized, the imprisoned Monad-Set can be freed from Demiurge-Ra's shackles and presumably lead the faithful into some kind of paradise. I'm not sure how that would look, but I imagine it'd be a state of pure spirit and bliss or the like.
The Path of Subversion just follows different methods, but mostly agrees with the theology. It sounds to me that they're unpopular with the main road because those consider individual corruption an art form, all Biblical Serpent-like.
Meanwhile, the Road of Apep do not follow the Gnostic liberation model (much?). They're mostly just chaos worshippers in the true sense, in that they consider a state of chaos a sacred experience and form of being where you're untouched by Ra. I'm guessing they'd still pay lip service to the revival of Set and liberation and such, but they're mostly living in the present. This also explains the hierarchy thing. The Road of Set wants to submit to Monad-Set, hence why they're hierarchical, and they can also work more effectively towards that goal with a higher level of organization and structure. Since chaos is not sacred to them for its own sake, that is not a betrayal of their beliefs. Whereas the Road of Apep views Set as less important, just a symbol or metaphor for chaos, which is everywhere, so they can submerge themselves in it everywhere and don't need any particular authority to follow.
Neither variant believes in freedom as we conventionally know it as a goal for its own sake, though it is an adjacent concept, especially for the Road of Apep, I would imagine.
As I understand, the Ministry is basically just the Road of Apep under a fancy new name, or rather, its logical conclusion. Because they mainly worship chaos, not Set in particular, they have an easier time breaking away from that aspect of the faith.