There are also limitations on what accommodations can be requested. If you took a job mowing lawns and then had a religious belief against harming living plants, you wouldn’t collect paychecks while you watched your coworkers mow lawns. They would have to find other work for you if they could, like raking leaves or lawnmower maintenance. If they didn’t have that work, then you wouldn’t have a job.
The raking leaves example was to make a point. For a programming job you could be exempted from using AI tools to do the work, but you would still have to do the work at a reasonable standard.
Plenty of programmers don't work at a reasonable standard; See, for example, every security incident ever, proliferation of slow electron apps, commercial software that flat-out doesn't work properly.