The non-men who were exposed believe oblivion is a lie, but we have seen that even erratic can attain it.
Since that's the only one we've ever seen manage it, for all we know only an erratic could attain it.
I honestly don't think we have enough information here to answer why the Inchoroi aren't ciphrang.
You are missing the point. The mechanics of avoiding damnation are not important.
We know the Inverse Fire is a tool of control. It's a compelling truth, but not the whole truth. Any Dunyain knows the value of partial truths in conditioning via deception.
The Inchoroi are conditioned to believe there is only one way to save their souls because of that. Extermination.
We know that Oblivion is an option. They deny that.
We know that Redemption can come from the one God or the Hundred. They say EVERYONE is damned forever.
We know you can level up your soul. They aren't interested.
Logical induction dictates being careful with immortality means not dying means no damnation. They would rather render themselves extinct trying to shut the world.
Maybe exterminating everyone and erasing history will work to save their souls, maybe they are doing it to free the progenitors from Hell, or maybe the progenitors just want to terraform planets.
Point is, their mission is focused to one goal only, the Inverse Fire is there to keep them on track.
Happily for them, the Dunyain want to do the same thing in pursuit of a Self Moving Soul. The Inverse Fire is barely required to get them to join according to Kellhus PoV in TTT.