Via Jim Henley I found this piece by Julian Sanchez and then this one by Dennis Prager.
I must say that I think that Prager is being ridiculous. I think that it is reasonable to allow a Muslim to be sworn in on the Qu'Ran. If the U.S. people do not like this, then they ought not to elect Muslims. Prager says that Jews and secularists have long been sworn in on a Christian Bible, but I do not see why that matters. If true - and I do not know that it is - it is probably because they decided not to object to it. If a Jew asked to be sworn in on a Torah, I doubt that most people would mind. If they do, then they ought not to elect Jews.
He also tries a reductio ad absurdum by asking what if we elected a Nazi who wanted to be sworn in on Mein Kampf (he actually says "a racist," but I think that it is fair to say that someone wanting to be sworn in on a book written by Hitler would probably hail from the Nazi wing of the racists). It does not appear to have occured to him that if we elected someone who believed in Nazism, what book he was sworn in on would be the least of our problems.
In fact, if we read Prager's piece, Prager nowhere suggests that non-Christians were not allowed to choose a different book, just that they chose not to object (and as I recall, John F. Kennedy was sworn in on a Catholic Bible rather than a King James Version, so I do see that there have been some accomodations made.
This does not mean that having an official sworn in on the Qu'Ran mnight not be troubling for various cultural reasons, but if it is a problem, then surely electing a Muslim to higher office would be a bigger one, and the fact that people voted for a Muslim should be the real issue, not the fact that the Muslim takes his faith seriously.
That is all.