Whole Sort Of Genl Mish Mash
Where to start?
Chief Justice Berger developed a test that would come to be known as the Lemon Test to determine whether a law violates the establishment clause of the Constitution. (1) The statute must have a secular legislative purpose, (2) its principal or primary effect must be one that neither advances nor inhibits religion and (3) it must not foster "an excessive government entanglement with religion."
The key measures in this test are "primary" and "excessive" (difficult to delineate at times). This is why Judeo-Christian symbols and practices that might have encroached into public life, but are primarily of historic significance, have been found to not violate the establishment clause.
While I'm not crazy about the Lemon Test, I think it is a reasonable compromise. I believe the Supreme Court recognized that, while the establishment clause fixes a wall between the sacred and secular when it comes to government, that wall can be a moving target at times. I think it is also worth mentioning that a forced syncretism violates the establishment clause as well.
Second, I think it is important to distinguish Muslims from Islamists (I do not believe the latter are true Muslims) and then ask whether either of the two are capable of making a true oath to uphold the Constitution of a representative republic. I grew up with several Muslims and spoke often with them regarding their faith. I believe whole-heartedly that any of my friends could truely swear to uphold the Constitution. The latter, however, is iconoclastic, and the Islamiste sharia is incompatible with our most basic sense of liberty. In an Islamist state, for example, women are often regarded as property or have the legal status of minors (thus, having few, if any, rights).
I think the real danger is that we, as Americans in general, seem to get so caught up in symbols that we forget the salient points. The French actually do a much better job of differentiating Muslims from Islamists, and have been doing so for a long time, while Americans are only now beginning to recognize the Muslim/Islamic people are not the same as Islamist people.
So I don't think the issue is so much whether the legislator swears on the Bible or the Koran, but rather whether the legislator is capable of swearing a true oath to uphold our Constitution. It is true that legislators are elected to represent the people who elected them, but they have a responsibility to uphold the Constitution first and foremost. An Islamist might be able to accomplish the first, but could certainly not accomplish the second. Given their way, all women would be veiled, non-citizens, and non-Islamists would have few or no legal protections.
While I agree with you that one can argue that, in many ways, the United States was founded on Christian principles, I think the argument is less convincing than some might lead you to believe. Granted, intellectual heavy weights like Dr. D. James Kennedy ascribe to this view, it is difficult to read the writings of Paine, Franklin, and Jefferson, and then read the Declaration of Independence and Constitution, without recognizing that the language therein is, at best, a Deistic compromise. True enough, many early government leaders didn't share such Deistic views of separation (the establishment of a Congressional chaplain is an indication of this, for example). If you read enough of Madison (a Christian), you will find that he agreed with the Deists on this point more than he disagreed.
And, Stephen, again I would point out that all of Islam is not anti-reason in the same way that all Christianity is not anti-reason. Remember, it was Islam that preserved Aristotle, science, and philosophy during the Western Dark Age. There is a rich tradition in Islam, and, sadly, this tradition is at a dire risk of being lost as the Islamists gain in influence and seek to purge those influences from the Muslim world.