Logic in an atheistic worldview

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Most, if not all, existentialist philosophers.

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OK, I was pretty sure you were talking about Sartre etc. Rest assured that what they have in mind when they say the "universe is irrational" is completely different from what I mean when I say it. It's perfectly possible for the universe to be both absurd (in the Sartre sense) and ruthlessly logical at the same time.

What I'm saying is that the universe is ruthlessly logical (laws of physics etc.). One of the results of this is that the universe has no interest whatsoever in our human desires. This, I believe, is what Sartre was getting at with his talk about absurdity (the lack of any relation between our desires and the universe's desires).

Feel free to correct me if I'm wrong about Sartre's POV. My knowledge of his writings/ideas is rather limited. Nevertheless, he was mostly talking about human desires and how they relate to the universe as a whole. I'm just talking about the universe as a whole. Human desires don't enter into it when it comes to the fundamental validity of the rules of logic as far as I'm concerned.