I'd agree that the 2 currents are the Bible current and the Greek/Latin current, though I'd hesitate to call the latter secular.

I think, grammatically, we have
Into (a canon based in the Bible and the Greek and Latin classics,) a religious and a secular canon ... entered a new text that belonged ... in both currents and in neither.

(Parentheses added for clarity, plus ellipses for subordinate clauses that mean we lose track of whatever it was the sentence was about.)
It's not the clearest pair of sentences.