The Constitution requires members of Congress to take the oath or Affirm they will uphold and support the Constitution of the United States. Many other office holders through out the country are also required to do likewise.
Most choose to swear on the Bible, Some Jewish members chose to use the Torah or other books of faith.
Some non Christians or Jews have chosen to affirm support for the Constitution with hand on the a Copy of the Constitution. All sound good to me, although I might chose the latter if I were the position but a Bible would due if asked to do so since it is the book along with the Torah it contains, that codifies western morality.
However, allowing member of the Islamic religion to use the Quran seem very troubling to me as well as disingenuous by them in my view. I think the following few statements of fact quite clearly reveal the conflict.
- Sharia law is and integral part of Islam.
- Sharia law is in many ways in conflict with the US Constitution.
- No one should be expected to take an Oath on the Quran and be expected give preference to the Constitution before Islam.
- No one can expect a follower of Islam to hold the Constitution above Islam while taking the Oath on the Quran.
- According to Quran 4:29, Muslims are obligated to lie when it serves their purpose, especially to the infidel.
I have discussed the last bullet in detail with Bosnian and Egyptian Muslims, trying to understand how to do business with middle eastern. Never could figure out how for sure, for sure.
I think the first to take Oath of office in the Congress was in 2006 on the Quran interpreted by Thomas Jefferson, as did the one if not both of the current Muslim members of Congress.
I do not think the good works of Jefferson matters in this question.
https://www.meforum.org/2095/islams-doctrines-of-deception
https://www.crf-usa.org/america-responds-to-terrorism/the-origins-of-islamic-law.html
https://www.cnn.com/2019/01/03/us/congress-swear-in-religious-books-trnd/index.html