"Non-fiction has numbers", we were told.
I'm not sure Dewey attempts to separate fact from fiction -- just to categorize the author's intent (or assertion).
In addition to the Christian Bible, the "non-fiction" section also contains religious texts that refute it. And New Age crystal vibration harmonic ecstasy stuff. And Dianetics.
The wide disagreement on "fiction" vs "non-fiction" is probably not a solvable problem. See also: a world map, at any time in recorded history.
That's not to say the line isn't murky, but that's true of any human classification system.
Speak for yourself. Several atheists including myself read some of the Bible for our book club. In particular the wisdom literature has value as a fiction removed from the religious context. Beyond that, the Bible is the earliest work we have which exhibits several tropes, and western art has been heavily influenced by it.
Fictional works are organized alphabetically by the author's last name