Please oh please oh please oh please can we not get into yet another iteration of the "war of the quotations" about whether or not any individual one of the sacred and holy Founding Fathers was a Christian, or a "real" Christian, or "saved" or whatever. I've seen a thousand of those threads and they all end up with the same cut&pasted lists of quotes and they never go anywhere and nobody ever learns anything or changes their mind.
If we're going to talk about the ins & outs of the current situation in the United States vis a vis the separation of Church & State, and the vaious legal tests that have been developed to determine if a particular piece of legislation is or is not out of bounds, the words of the founders don't help much anyway.
What we need is a little bit of intellectual rigor. A willingness to step back from the emotionality of the issue and break it down into the little bitty legal pieces that make up the greater whole.
Herewith, a little review.
"Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech"
Now - that's three (3) things.
First that Congess can't make a law that would tend to establish one denomination, or one relgion, or even general religiosity over the whole country.
AND
Second,that Congress can't make a law abridging freedom of speech, (and having an open Bible out for the purposes of "show" rather than for actually reading it can be interpreted as a form of political "speech")
BUT
Third Congress is also forbidden to make any law that would interfere with an individual freely exercising their own religion.
SO
If Congress made a law that all Americans had to have an open Bible on their desk, that would be out of bounds (violation of the establishment clause)
If Congress made a law that all Senators and members of Congress had to have an open Bible on their desk, that would also be out of bounds. (violation of the establishment clause)
If Congress made a law that anybody at all was prohibited from keeping an open Bible on thier desk, that would also be out of bounds. But pay attention now, NOT because it was a violation of the free exercise clause. Unless they could show that public display of an open Bible was an essential tenet of their religion, the free exercise clause doesn't come into it.
The reason that it would be out of bounds is that forbidding the display of an open Bible would be an abridgment of free speech.
(Secret insider information: almost all of the case law regarding the free exercise of religion actually ends up getting decided on the basis of the right to free speech.)