A person not a citizen of the United States by birth or inheritance must obtain citizenship via naturalization. The process for becoming a naturalized citizen involves an oath of allegiance:
"I hereby declare, on oath, that I absolutely and entirely renounce and abjure all allegiance and fidelity to any foreign prince, potentate, state, or sovereignty, of whom or which I have heretofore been a subject or citizen; that I will support and defend the Constitution and laws of the United States of America against all enemies, foreign and domestic; that I will bear true faith and allegiance to the same; that I will bear arms on behalf of the United States when required by the law; that I will perform noncombatant service in the Armed Forces of the United States when required by the law; that I will perform work of national importance under civilian direction when required by the law; and that I take this obligation freely, without any mental reservation or purpose of evasion; so help me God."
A Muslim, whether practicing or not, must be presumed to be unable to "swear this oath" as that term of art is typically understood. Why is this so?
Islam has as a basic tenet that there can be no other allegiances superior to Islam. It is analogous to the First Commandment of Judeo-Christianity. But the oath asserts that the person swearing the oath will "support and defend the Constitution and laws of the United States of America against all enemies, foreign and domestic", and "bear true faith and allegiance to the same". No Muslim can do this, since it (potentially) places Islam in an inferior position relative to the Constitution.
But many Muslims do swear this oath. Have they committed perjury? To non-Muslim eyes, the perjury is clear, but to Muslims (whose first and only duty is to Islam) the issue is not-so-clear. The Koran, the 'holy book of Islam', carves out an escape clause: taqiyya. Taqiyya, simply put, allows a Muslim to lie to an infidel (any non-Muslim) if doing so advances the cause of Islam.
Further, they cannot "take this obligation freely, without any mental reservation or purpose of evasion", since evasion is exactly the purpose of obtaining citizenship. Obtaining U.S. citizenship is seen as a necessary first step toward the primary goal of Islam: establishing a world-wide caliphate governed by Sharia law. Taqiyya is permissible.
Summarizing: Muslims who take the Oath of Allegiance to the United States can only do so by resorting to taqiyya, an action that otherwise constitutes perjury and invalidates the oath ab initio.
No Muslim should be offered United States citizenship under any circumstances. Muslims who have been granted citizenship via naturalization should be immediately de-naturalized. Muslim citizens-by-inheritance should be considered national security risks.
