[T]he Muslim woman has actually thought through the implications of her faith enough to actually want to persuade others, and has ranked the different reasons for disagreement for their plausibility. This is the same kind of person who would watch that they're going above and beyond to adhere to their faith's requirements.

On my reading, this implies that, if you think that the woman is devout, you should think it less likely that Yvain lied when he reported his conversation with her.

Here's why:

Let ARGUES be the proposition that an arbitrary Muslim woman in Cairo is willing to argue for creationism with a stranger.

Let DEVOUT be the probability that an arbitrary Muslim woman in Cairo is devout---that is, that she "would watch that [she's] going above and beyond to adhere to [her] faith's requirements."

You consider p(ARGUES | DEVOUT) to be low enough to justify calling Yvain a liar. Thus, DEVOUT must refer to a devotion strong enough to make p(ARGUES | DEVOUT) this small. But, I claim, you should consider p(ARGUES) to be even smaller.

On my reading, you assert above that, if the woman argues for creationism, she is very likely to be devout. That is,

(1) p(DEVOUT | ARGUES) > 1 - epsilon,

where epsilon is small enough to justify your omission of any phrase like "very likely to be". On my reading, this makes epsilon small enough so that, in a cosmopolitan city like Cairo,

(2) p(DEVOUT) < 1 - epsilon,

where, again, DEVOUT refers to a devotion strong enough to make p(ARGUES | DEVOUT) small enough to justify calling Yvain a liar.

Putting (1) and (2) together gives

(3) p(DEVOUT | ARGUES) > p(DEVOUT).

Therefore,

p(ARGUES)
= p(ARGUES) * p(DEVOUT | ARGUES) / p(DEVOUT | ARGUES) [multiplying by 1]
< p(ARGUES) * p(DEVOUT | ARGUES) / p(DEVOUT) [by (3)]
= p(ARGUES | DEVOUT) [Bayes's formula],

so that p(ARGUES) < p(ARGUES | DEVOUT), as claimed.

ETA: Edited to correct typo in derivation.

ETA2: Sorry, more corrections to the argument . . .

This is the same kind of person who would watch that they're going above and beyond to adhere to their faith's requirements.

You should be aware that when you write

(1) "The kind of person who is an X is also a Y.",

many careful readers are going to read that as equivalent to

(2) "All people who are Xs are Ys."

Come on, this is basic Bayesian probability theory here. You should have dropped the rhetoric of "you think X implies a 100% probability of Y" a long time ago.

Indeed. No one here had said anything about 100% probabilities. If you want (1) above to be read as shorthand for

(1') "The kind of person who is an X is also a Y with probability 1 - epsilon.",

then you should reciprocate by reading (2) as shorthand for

(2') "All but a (1 - epsilon)th of people who are Xs are also Ys."

If you want to dispense with "most likely", "nearly all", etc., then you should allow others to do the same.

I certainly could have made the basis for that belief more clear, but you also should have applied the principle of charity and thought about the possibility that it wasn't just a misreading, and that there are reasons to infer someone is a "devout Muslim" other than "oh, someone told me with those exact words."

This seems a fair summary of your view: Any Muslim creationist is so likely to be a cultural traditionalist that, when Yvain reports meeting an exception in Egypt, you may confidently accuse him of lying.

And that, I maintain is a baseless inference, albeit a probabilistic one. One shouldn't throw around accusations of lying without justifying strong confidence in such an inference.

Someone this familiar with their faith and aware and disdainful of the specific arguments against it,

This does not seem like an accurate reading of the post. "Aware and disdainful of the specific arguments against it"? The woman in the story is portrayed as unfamiliar with atheism and atheists, not familiar-yet-hostile. She doesn't even attack the argument from biblical contradictions.

it's just that the consideration didn't end up favoring Yvain.

So I take it that you've been to Cairo or other modern middle-eastern cities, or read extensively about them? I find it hard to see how you could be so confident in your domain knowledge otherwise.

I also factored in his past tendency to embellish facts.

What past tendency? Do you have links?