“What does an agnostic or atheist or an adherent of non-Abrahamic religion do when asked to make the oath for admission to Congress?”
Good question. Article 2, Section 1, of the US Constitution:
>Before he enter on the Execution of his Office, he shall take the following Oath or Affirmation:—“I do solemnly swear (or affirm) that I will faithfully execute the Office of President of the United States, and will to the best of my Ability, preserve, protect and defend the Constitution of the United States.”
This is about the President. The Oath for Congressmen and Senators is not given in the Constitution, but the same principle applies. A person is never obliged to swear an oath. One always has the option of affirming.
Also, the traditional coda, “So help me God,” is not in the original text.