Many of my Quaker friends won’t swear oaths (including “so help me God”), but instead state that they will [do whatever it is they’re being asked about or inducted into].
I needed to have someone take an oath once and of course I didn’t have a bible, so I used a copy of Vanity Fair and made her say “so help me Jackie O.”
When I was in 7th grade, we had a mock trial in a science class, and we swore each other in on a textbook and ended it with “so help my Life Science grade.”
Arizona Senator Kyrsten Sinema, who was raised Mormon but now claims to be areligious, was sworn in on copies of the U.S. and Arizona constitutions. She showed up dressed and made up to look like Marilyn Monroe, in a minidress and thigh-high boots, and is openly bisexual. I’m mentioning all this because she was sworn in by Mr. Mother, AKA Mike Pence.
I think you might have your photos confused. Sen. Sinema’s wardrobe when she was sworn in got her the nickname “Senator Madonna.”
Her thigh-high boots look like she was dressed for walking through slush.
Swearing on the Bible is simply political theater. Politicians do it to cater to the majority population who are Christians. They know that any appearance of not being sufficiently devout has usually been political death. It’s the same reason that “In God we Trust” and other religious slogans in public use have always been allowed by the Supreme Court under the guise of “ceremonial deism.”
It’s not law, it’s pandering.