It's not really a question of an oath not being 'legal'. Fears were raised by constitutional experts that Obama's presidency might not have been constitutionally sound in view of the errors in the oath-swearing. It's happened before - Obama isn't the first president to fluff his lines.
As for state and church being separate - they are, but if you're going to swear an oath and you're a committed Christian, what better way to do it than on your holy book? Tradition also has it part to play - the bible was the same one that was used by Abraham Lincoln.
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