That's all fair, I was just trying to think of a counterexample for the sake of the discussion. I would certainly say that atheism in and of itself is a fundamental rejection of an absolutely essential component of "culture" as it has been defined for the vast majority of human history. In this context, you would certainly think it is fundamentally culturally left wing in trying to deconstruct what has existed before and usher in something new.
I think you're conflating one's personal beliefs regarding the existence of God with one's political beliefs regarding the appropriate role of religion in society. Until a few decades ago, there had, down the centuries, undoubtedly been many 'closet' atheists who nonetheless fully participated in religious life precisely because it was such a central part of the culture, and who may well have been politically conservative.
To give a particularly famous example, you can make a very strong argument that David Hume was an atheist, and he was also frequently held to be a Tory! (Admittedly his public commitment to Christianity was weak enough to draw the suspicion of his contemporaries, so he is perhaps not the best example of a true 'closet case'.)
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