The important thing about taking the Oath of Office is that it is a solemn Oath.
The traditional Christian belief was that if you violated a solemnly sworn oath to God, you went to Hell.
Well, I don’t know how much leverage that has with many people these days. But that’s certainly the kind of solemn oath you want—something that will be taken seriously, so seriously that a violation means the loss of salvation.
That’s why, for instance, a POTUS swears to uphold the Constitution, but swears to do it on the Bible. The Bible is not necessary, but it’s a reminder that this is an oath taken with God as witness—and enforcer.
To them, (not to those who gave us the constitution and other very important things like taking a real oath to God) the only view of reality upon which our freedoms could stand was the world view that their was a Creator to whom we will answer, (even for things meaningless to liberals, such lying under oath).
All exceptions only prove the rule.