Here is how the main Church is laid out in my homebrew world:
Culturally, there is a slight male-dominant tendency. Not as much as real world history, but enough that women adventurers are remarked on and noted, and some look at them as social misfits.
The Church, overall, is NG. There are various sects with slightly more Lawful, Neutral, or Chaotic inclinations. The main sect is considered the Orthodox sect, and represents the most common "practical" NG orientation.
There are various lesser sects, all of which are allied with the Orthodox sect in the defense of the faith. In terms of dogma, all of these sects believe and teach the same core tenets. Because of their different orientations, each sect supports a slightly different set of Prestige Classes (supports means that the sect is able to train someone in that class). All of them support the Templar and Warpriest classes.
Patriarchists (LG/N): This sect emphasizes the role of male deities and male historical religious leaders, while also minimizing the role of females. This group also seeks to reduce the freedoms of women in society, placing more responsibility in the hands of "the more capable males". Inquisitors and Exorcists are common Prestige Classes supported by this sect.
Matriarchists (CG/N): This sect does not try to overemphasize the role of women the way the Patriarchists do with men; instead, this sect is organizaed around the idea of preserving the proper credit for the role of women in the Church. They also work to increase the range of options for women in society. Holy Liberators are supported here.
Free-Thinking (CG/N): This sect advocates that the best way to spread the faith and improve society is by educating anyone with the talent for magic. While recognizing that magic is a tool that can be used for good or ill, they feel that mages educated by the Church are more likely to use their skills for the common good, and will be more likely to help put down the maverick mages that abuse their abilities. Mystic Theurges as well as some Arcane-based classes are supported here.
Anti-Magist (LN): This sect believes that only those chosen by the gods should wield any magic. Secular mages are a danger in their eyes, and need to be controlled. Mystic Theurges, Exorcists, and Inquisitors are supported.
Re-Unionist (LN): This sect wishes to re-unite the local Church with its former parent, a more True Neutral aligned version of the Church. A schism hundreds of years ago split off the local good-aligned local Church from its parent organization. This sect wishes to see the Orthodox (and other sects) submit to the authority of the original parent.
Hope that helps.

Note that the political differences have nothing to do with the doctrines of the Church -- religiously, one sect is the same as the others. The differences are all social and political.