I was told that this may be an interesting premise for a new question. I had the following interaction in the comments of this question.
It always striked me as odd that a secular state like the US would use a religious document as such a key part of a government proceeding. (assuming they still do that)
This was in reference to the issue of swearing on the Bible in the US. A comment to which David Siegel replied
They do still do that. That would be a good separate question. The basic reason is that this procedure was inherited like much US court procedure from England, and for much of its existence the UD had thought of itself not as a secular state, but as a multi-faith religious state with built-in toleration, and only in the 20th C has much of that toleration been actually enforced. Until 1867 states were free to have established religions, and some did. (Mass and Maryland are examples.)
The mere fact that some states actually had established religions, even if it ended 160-odd-years ago is to me incredible. The premise of the US seems to be a country free of a monarchy and established religion seemed to be a big part of what makes the US, the US, or at least a big part of how it is sold to foreigners wanting to live there.
So the idea that the US for a certain part of it's history did not think of itself as a secular state, but a multi-faith, tolerant state seems a very intriguing one. Also it seems so completely antithetical to how it is perceived today (Not the tolerant part, but the multi-faith part).
So back to the issue at hand. If we accept that the US has moved away from the idea of a multi-faith state and indeed into a secular one, how are these vestiges of the old system still enforced or defended?