Here in CA, it's pretty clear that people should have a choice to either swear or affirm, nor is there any requirement to raise one's right hand. In your kind of a situation, I might have asked the notary to show me where that requirement is written in our handbook. On the other hand, I might have just done as she asked to get it over with and moved on. But if a person's beliefs were opposed to "swearing" under oath and they instead wished to "affirm", then I'd say a push back would be appropriate.
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