From everything I've read, Prager is wrong and inconsistent in many areas of his article. Most of them were addressed by Eugene Volokh. But there is one aspect of this story that I haven't seen mentioned.
The purpose of the book that some (not all) public officials swear on is to show the seriousness of the oath, not as an affirmation of the contents of the book. The use of a Bible or Koran or Tanakh is tangential to the point of the oath - which is, in this case, to uphold the Constitution of the United States. Here is the text with the words in italics not being necessary:
I do solemnly swear (affirm) that I will support and defend the Constitution of the United States against all enemies, foreign and domestic; that I will bear true faith and allegiance to the same; that I take this obligation freely, without any mental reservation or purpose of evasion; and that I will well and faithfully discharge the duties of the office on which I am about to enter: So help me God.If Ellison believes that the Bible is a corrupt and incorrect document, which is what Islam states at least in reference to the Old Testament, then insisting that he take the above oath on a book he doesn't believe in is much worse than his swearing to uphold the Constitution on a book that he believes passionately in. In other words, his swearing on a book he doesn't believe in has the same import to him as swearing on a comic book.
The fear that some have about Ellison is whether he, as a Muslim, has the ability to uphold the Constitution. There may or may not be contradictions between Ellison's flavor of Shari'a and the US Constitution, and that is a reasonable question to ask (just as some worried that JFK would put his Catholicism above his patriotism.) But his swearing on a Koran has nothing to do with that - on the contrary, it indicates that at least to him, the two are not mutually exclusive, a conclusion that could not be made if he was forced to "swear" on a book he has no belief in.
Slightly more problematic is the idea that he will replace "So help me God" with "Allahu Akhbar." While I have no problem with the words "God is great" themselves, it is very troubling to think that the very words that have been shouted to accompany the murders of thousands of Americans and other innocents worldwide should be uttered in Congress. This is not a logical argument but an emotional one, but it is one that I cannot personally let go so easily.