I would not use LLM and generative AI systems in my programming, for several reasons.

If you can do it better without the AI, then you should not be forced to use it anyways, or tracked for using it. (Even if you only track the statistics, and how much time it takes, that is not sufficient because you must figure out if the result is actually good, and any other related issues, including e.g. costs and energy usage, testing (not all kind of testing could be automated), kinds of statistical bias, etc.)

In general, not all kind of religious exemptions would mean you would be able to do the job, but in this case the exemption is reasonable if she is competent at computers; you shouldn't need the AI systems to do it even if they insist that you should. If they have a religious exemption they should show that they could still do that job or else to leave that job (rather than being forced or coerced).

Thare are both religious and non-religious objections (as well as people of the same religions who would not be opposed, since they are different people even if religion are same; there are also some more nuanced opinions). (There are more religious objections than only Unitarian Universalists and Catholics; I have looked and found some opinions by people of a few other religions, and there are probably more than that too. Different people can also have different opinions regardless of whether or not you are religious or of a same or similar kind of religion.)

Ummm… Unitarians in general do not believe in anything specific, so this seems arbitrary but don’t worry she will probably be fired for underperforming soon anyway

This is the dumbest timeline…

Imagine working with this person. At a certain point you just can't do the job. What if a religious Jew wants to work at a butcher shop and refuses the handle pork. Why does everyone feel like they're entitled to do a particular job, making everyone else's life considerably more difficult