When in the course of this nation did that change? Because that used to be the oath taken and a real Bible of OT and NT was placed under the left hand while raising the right hand ... I did this ritual many years ago in a court just as I have described it. What influenced the change to no longer use the Bible or require the fealty? And without the fealty then you ahve a self-fulfilling loop where only threat of being discovered in the here and now prevents lying to achieve whatever goal one has. Do you see the difference in what is at work in the human value system when that fealty to your Cretaor is removed for the purpose of 'separation of church and state'?
"When in the course of this nation did that change?"
Actually, if you'll look at the oaths of office in the Constitution, you will find that they contain nothing about Bibles or deities. One may swear or affirm any oath of office in the U.S.A.
In the courts, the change took place in various places at various times.
Think about it. Only Christians could swear an oath on the entire Bible. Even some Christians don't swear any oaths at all.
Hindus, for example couldn't swear an oath on a single diety, and atheists and agnostics would be telling a lie if they swore an oath to a deity.
You are not required to use a bible or add the words "so help me God" in any court. If you think about it, you'll understand why. In most jurisdictions, no Bible is even offered. Even if it is, you may simply say to the Bailiff, "I will affirm my oath."
Same is true in the military. You needn't invoke the name of any deity in your oath when you join the military.
Not everyone in this wonderful country is a Christian, so the oaths you remember do not apply to everyone. Think about it.