I like the religion descriptions in general!

Of course for some parts I view the religions differently:
For
Edenism, I'd restate their "mission statement" as "reshaping Chiron in Earth's image" instead of "expanding the human presence on Chiron".
Also I'm not sure I agree with your subgroups within the Edenist religion. Your "Natural" Edenists may sound a little too similar to Voice terraforming/chiroforming goals. I do agree you can hace different views within Edenism: one side's goal would be to increase the human population size as much as possible, and their terraforming could as a consequence focus on monoculture farming. The "natural" Edenists could have a more romantic vision, and want to create an ecological (but terran) paradise, which means planting forests, and no focus on population growth at all costs. Deirdre would have this view in the first years on Chiron, before signs showed up the Xenofungus was something special. In a way, the Edenism religion can contain both contemporary environmentalists and non-environmentalists. They both think however that terran and chiron ecologies are incompatible, and that spreading an ecology friendly to humans necessarily means destroying the Chiron ecology. That's why I disagree with your description of the "natural" edenists.
Homo Superior
Who's Diegas Patel? You?
Basically I see two visions on what it means to be(come) a Homo Superior.
One you have covered: through genetics and cybernetics. The other vision (and the reason why Homo Superior is attached to Memetics) says that being a Homo Superior has nothing to do with improvements to your body, but rather is all about reshaping how you think. They favour a Nietzschean morality, and place heavy focus on creativity of all kinds and seeking knowledge: they try to think rationally, using the scientific method, all the time. SMAC's Intellectual Integrity quote fits in this vision.
Most Homines Superiores

would to a varying degree agree and follow both visions though.
Ascetic Virtues
Not much to add here. Perhaps mention that the philosophy draws inspiration from Buddhism and Daoism.
I disagree with the factions you think would like/dislike this religion. While I can imagine the Spartans running Ascetic Virtues, I rather see that faction as the paragon Homo Superior (though with a heavier focus on the genetics vision than the memetics vision, compared to Peacekeepers for instance). Also I can imagine not Morgan himself but certainly a portion of the Morganites following Ascetic Virtues. Puritan capitalists is nothing weird. IIRC it is said that protestantism in its early days for instance placed a heavy focus on work ethic and not consumption, which meant that capitalists had more money left to invest in new stuff. In any case, an ascetic morality can have synergy with capitalism.
Voice of Planet
I disagree with your statement that "This religion/philosophy was founded amongst the gaian faction soon after the discovery that planet’s fungus and mind worms made up a large, thinking, neural network." Personally I think full realization of what Planetmind is and its connection to psi, mind worms, and xenofungus may come as late as the Centauri Ecology technology. Before that, it are only suspicions.
You could elaborate the description a little by mentioning contact with Planetmind only came gradually. At first contact would only consist of inexplicable dream fragments (such as in the Lalala quote, when Planetmind still had a very childlike consciousness). Later contact could be reached through a trance and meditation. At this point (Centauri Meditation) it began to become a religion. Still, because the ways to achieve a contact were all still very subjective, the Voice was at first a very mystical religion, and its followers were heavily mocked by the University as a bunch of drugged hippies. Only later it would gradually become apparent the Voice followers were actually on to something real.
Oh, that reads pretty neatly, but I'm not sure how good it is to have the faction leaders mentioned. While the religions are strongly tied to them, they're not locked in
I don't necessarily agree with that. Even if actual games play differently, there's nothing wrong with having an "official" history.