There's a clause that explicitly bans religious tests for federal public office[1], and a landmark SCOTUS case clarified that state governments cannot do this either[2].
No, in addition to the clause which directly prohibits religious tests, there is no clause which does anything like that; the required oath or affirmation is:
“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.”
No supreme being required or even directly relevant. You may be confusing the Presidency with Alcoholics Anonymous, which requires acknowledging a “higher power”.
I do that all the time.
“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."
That’s it.
“So help me god” is not part of it, despite some tradition. Not all presidents have used bibles or sworn to a god.
https://en.wikipedia.org/wiki/Oath_of_office_of_the_Presiden...
Oaths of office for other federal positions do contain the phrase "so help me God," but so far as I know there has never been a problem omitting it; I had several friends in Federal service do so.
Quite the opposite. The first amendment's establishment clause prohibits the government from "establishing" a religion, i.e., forcing religious on someone.