Makes senses... but if she was adopted, then how would it explain the fact that young reimu was wearing her miko uniform at the age of (roughly) 5/6 years old? i feel that in japan (and gensokyo) it would have been way to early for her to give those clothes until her teenager years or something...
This makes me think of Littles Nuns...'s artistic take on religion, since, quoting that troupe:
Artistic License – Religion: In real life, a woman must be 18 or older before she can take the vows and become a nun. While young girls living with the church (perhaps as orphans) isn't unheard of, they wouldn't wear the habits until they take those vows.
I feel this can also apply to shrine maidens too, regardless if they're born in gensoyo or the outside world too.