On Texts, Sacred and Otherwise, and Oaths of Office.

What makes the Bible or another sacred scripture valid for a binding oath or affirmation, and the Constitution does allow for an affirmation instead of an oath, is that the scripture is immutable and not subject to alteration according the changing interests of the person holding it. While King James and others have sponsored translations that codified secular interests the principle holds that the content is considered as external to and unchangeable by human will.

The Constitution fails that test. It is designed to be amended by politicians to reflect changing needs and interests, although the process is deliberately made complex.

The Koran may be objectionable on the grounds that its content may be antithetical to those of the Constitution, as might be some text sacred to a future Rosicrucian, but that is a harder argument to win than a claim that swearing on the Constitution is sufficient. Is the politician who so swears then bound to never support any future amendment?

Even an absolute monarch when consecrated is called to appeal to be judged by some power greater than their own Will. Detroit's Congress Member Ilhan Omar swore on a Koran. She would be judged by an impersonal and unloving god and by comparison to the standard of a bloody and duplicitous tyrant but that is a standard, which others may fear, that is beyond her control. Senator Sinema is held to no standard but her own.

CBS News: "Kirsten Sinema takes the Oath as Senator on a copy of Constitution instead of Bible"