'Spiritually uninstitutionalized' seems to be a play on 'unchurched,' which is a word that American evangelicals have traditionally used to refer to people who are not members of a church. The underlying syntax suggests a verb 'to church someone,' meaning to make them part of a church, bring them into the church. To me that implies that it's something you do to someone, perhaps even willy-nilly, not something they do for themselves, which is why I am not fond of the whole concept.
Here it's tongue-in-cheek and even broader, making clear that not only is she not a church member, she's also not a member of any other spiritual institution -- that is, a synagogue, a mosque, a Buddhist temple ... It's as if she has resisted being made a part of anything -- but of course that's one of the many contradictions within the whole paragraph, like that she's happy to be an original thinker, but she likes people who think just like her. The whole passage seems so cuttingly sarcastic that it's actually rather sad.
Does that help? If you need more help with the rest, make an effort to translate it yourself and we'll see what you don't understand.