What real difference does it make what he takes his oath on?
He, like 99% of the rest of them will not honor it anyway.
I, Loyal Citizen of the Republic, do solemnly swear (or affirm) that I will support and defend the Constitution of the United States against all enemies, foreign and domestic; that I will bear true faith and allegiance to the same; that I take this obligation freely, without any mental reservation or purpose of evasion; and that I will well and faithfully discharge the duties of the office on which I am about to enter. So help me God.