I don't usually look in poly-tics due to the amount of crazy, but was looking for something partticular when I ran by this.
People, the Constitution was ratified without the Bill of Rights because those were ADMENDMENTS to the thing. The country went several years without a Bill of Rights - first folks wanted to see how this new notion of governing would work out, and then they debated about just what "fixes" it needed to have an even more perfect Union.
Since there is no legal requirement that federal office holders swear "on" anything, what's the big fuss what they rest their hand on while committing perjury? (Yes, I understand the symbolism and all. It's just that for all the swearings-in on The Bible (whichever version and previously belonging to whomever) I cannot recall any $diety striking anybody with a bolt of lightening, a case of boils, or being eaten alive by a swarm of locusts for putting their hand on The Bible during the ceremony.
If you look at the actuial oath of office, you will see that there are no words "so help me $diety" at the end. A case might be floated that by saying those words the oath taken was improper, but who's going to really care?
stay safe.