There's also an already built-in way for differing sects to develop within even a hands-on church, and is recommended in the DMG or the FRCS:
Domains.
Take, for instance, Sune (CG, Greater Goddess, etc.). Her domains are, what, Chaos, Charm, Good, Healing, and Protection, right?
So, within her church are several separate sects, all of whom approach Sune in slightly different ways. There's the Seducers, who choose Chaos and Charm, who seek to spread and enhance the act of physical love. There's Heartwardens, with Protection and Healing, who seek to defend objects and places of beauty. Likewise, there are the Aesthetes, Charm and Good, who deal with the moral philosophy of uplifting beauty.
All of these groups share similarities, but all approach the worship of Sune in different ways - and all are favored by their goddess!