There are two (well, probably like ten) games being played right now in SA. Those in the secular gallery trying to wield the levers of power to gain an upper hand, and those in the spiritual gallery sawing off the levers forever. A lot of people like SA as a purely religious force. They joined because religion in BM can offer something apart from the usual political chicanery. It can help one really develop a character. I'm willing to bet, given the stagnation caused by the secular gallery's regular (ab)use of the levers, that those same people will hand the "victory" to the spiritual gallery.
The fact that SA has political power is in my opinion one of the things that make it different from other standard BM religions. Very, very few players are willing to sit through and write scores of theological disputes if there is no way for either party to "win" by enforcing itself upon the other; this is why most BM religions are dead boring and become little more than background flavor in a secular world. And yes non-political religions can of course make for good character development, but these characters will then typically act out most of their story within their realm (because there are only many long rp letters one can post before one needs to actually do something significant) leaving the religion a silent shell.
Also I'm not sure I agree with your characterisation of "spiritual" and "secularist" factions in SA. While I agree that many secularists on both sides of the recent conflicts are trying to pull the levers of SA to gain political power, I don't think any of those arguing that the Church should have no political power are anything more than secularists themselves- they don't want a more "spiritual" SA, they want one that keeps quiet and damned well out of their business. Most of the characters that have actually contributed to the "spiritual" side of SA in the past seem more in support of a political Church than against it, likely as Vellos said so that they can actually enforce orthodoxy rather than their see their various beliefs become essentially meaningless.
