Who says that they didn't?
I do. If you squint hard enough you can detect monotheism in any religious system at which point the term "monotheism" loses any meaning.
I'm using the conventional approach where religions like Judaism and Christianity (in spite of the Trinity!) are monotheistic and religions like Hinduism and Shinto are not.
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It's not clear to me how this "fairness" criteria is supposed to work. If you simply don't include S among the predictors, then for any given x in X, the classification of x will be 'independent' of S in that a counterfactual x' with the exact same features but different S would be classified the exact same way. OTOH if you're aiming to have Y be uncorrelated with S even without controlling for X, this essentially requires adding S as a 'predictor' too; e.g. consider the Simpson paradox. But this is a weird operationalization of 'fairness'.