In the US, nothing. Swearing in is a legal process with specific criteria, it’s extremely difficult to undo in general and something like a religious conversion isn’t legally sufficient to make that happen. When it does happen it would typically be a full replacement where the person is found to have not actually met the criteria for the position so whatever selection process put them there needs to be repeated rather than the swearing in process itself. Swearing on a religious text isn’t actually required in the US, it’s a First Amendment violation so everyone has a right to use a secular text or some other alternative if they want, the specifics don’t actually matter under the law so long as you are affirming your oath.
In the US, nothing. Swearing in is a legal process with specific criteria, it’s extremely difficult to undo in general and something like a religious conversion isn’t legally sufficient to make that happen. When it does happen it would typically be a full replacement where the person is found to have not actually met the criteria for the position so whatever selection process put them there needs to be repeated rather than the swearing in process itself. Swearing on a religious text isn’t actually required in the US, it’s a First Amendment violation so everyone has a right to use a secular text or some other alternative if they want, the specifics don’t actually matter under the law so long as you are affirming your oath.