While cooking may be an "art" cooking a previously set menu is not "art" or at least, it isn't "original art." Even if the recipe in question was their own creation. While the Chef may have a Freedom of Association/Religion claim they could assert, as far as their service is concerned, it revolves around their ability to perform a specified task in accordance with specified instructions.
Of course, that being said, there is cooking the food, and then there is presenting the food. Much in line with the photographer above, and why I'd personally not push to get a service provider to render services they've told me they don't want to provide me. After all, taking pictures is just point and shoot right? Well, there is a bit of difference between a professional photo and an amateur one, using the right exposure settings(with the right equipment), getting ideal focal lengths for what is being pictured, creating or otherwise working with existing lighting conditions, "framing the picture" and so on. Any one of those things, when just a little bit off, can turn a great picture into just a good one(or "lucking into" the reverse in the case of a amateur getting a great photo instead of just a good one).
So the Chef could perfectly select the ingredients, and perfectly cook the foods, but when it comes time to present the finished product, he half-asses the presentation, or deliberately screws with it. So while the food may otherwise be cooked to perfection, it looks like complete s___. Which is where a LOT of the artistry of cooking happens, but if you've told them that their personal views as an artist don't matter, well....
But this also goes back their claim as both professionals and artists, they probably take great pride in their work, and they don't to present anybody with what they think would be a sub-par product. So when they say they don't think they'd be able to perform to their usual standard on a given project or task, it's probably a good idea to heed the warning and let them reject the work.
Which takes us back to the bakery, cooking a cake doesn't take a lot of artistry(robots can, and now do, often bake cakes), but decorating it with original work does involve a human, and "Artistic" touch. If you want a cake, by all means buy a cake. If you want original work done, once again, you probably should avoid the "artist" who is warning you that they "don't think they'd be able to perform to the usual standard" in regards to meeting your request.
Heck I have a sister that used to decorate cakes for a grocery store at one point, its a skill she retains decades later and still uses on occasion. The skill isn't THAT rare, every grocery store in the country probably trains 1 to 6 people a year in how to do so. She also often does skip the "bake the cake" step by opting to get one from a store, and then providing the customization herself.
The internet is a wonderful thing these days, finding a cake decorator, rather than someone to bake the cake and decorate it, is probably far easier today than any time in history. So yes, on the bakery, the breakdown becomes: Yes, they have the right to refuse to decorate a cake in certain specified ways. No, they do not have right to simply refuse to sell a cake on any grounds other than inability of the customer to pay for it, or other more specific causes that are widely accepted reasons for refusing service. (No shirt, no shoes, no service; walking in while waving a gun around, etc)
