Does the word "nonsect" in the chorus hold any particular meaning, or is it Sawao just fooling around with his excellent English again?

I am guessing that he was having difficulty finding a word that rhymes with "perfect," and therefore made up a word that he thought would mean something in English. After all, while the closest English-language approximation is "nonsectarian," it makes little sense to say, "She's not affiliated with a specific religious denomination," as that makes little to no sense.

Considering the following lyrics, my best guess is that he meant something similar to "nonsecular," if not that word, which is kind of the exact opposite, but whatever - it may have been a word association thing.

Sawao is probably a sensible athiest, and therefore his perfect girl is also non-religious.

atheist*

However, as entertaining as that notion is, I'm inclined to say that that's not it. It makes more sense that he is saying that she is in some figurative sense divine.

I'm going with Sheer on this one.