Kinda half-asleep, but want to clarify some things.
So, I suppose this should be worked out now: is she, in all senses of the word, a god; or is god being treated as an extension of the 'Lunarians are disturbingly competent' thing? 
Your character is a god. People worship her, and she gains power from her faith. She's also extremely competent. Most other lunarians however fall on the disturbingly competent field, since they can't be bothered to gather faith from the filthy vermin that crawl the earth.
Since by Touhou canon, they're basically the oldest sentient creatures and have a habit of being revered like gods. 
Nitpick, but only one of them can claim to be the oldest, and that's because of her absurd knowledge on medicine. We know that before Kaguya, all other lunarians used to die of old age (that's why she was exiled to Earth, since she was the first lunarian to achieve immortality, which was considered forbidden).
The moon was impure as well. It was chosen as the lunarian base because they figured out it would be easier to purify because it was smaller. It still took centuries, countless sacrifices, and wiping out basically most of the moon's native life.
Also again, lunarians that are revered as gods are pretty rare, because most live in complete isolation in the moon. Only those those few that actually enjoy a stay on the "impure" world now and then gather followings.
