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Courts decide cases based on evidence, including any given on affirmation instead of oath, and by reference to man-made statute or binding precedent case law (including judgments by agnostics, atheists or even anti-theists) which evolves alongside changing social norms, and not by reference to a judge's supernatural beliefs or divine guidance (the latter of course being open to interpretive challenge). But if any judges are in fact biased for religious reasons (whatever that religion happens to be, which is a lottery) it's unlikely to be provable anyway. Abolishing a colourful traditional annual ceremony would make no difference to that.