Since that is not their reason for turning down the business then yes, saying you're doing it for artistic reasons would be a lie. And since their reason for turning it down is it violates their religious beliefs then I can understand why they would not want to resort to falsehoods. And the government should not encourage them to do so.
If I have religious reasons for not being artistically interested in that commission, then it is not a lie to say I am not artistically interested.
No different than saying I’m not interested in going to a party. It might be because I can’t stand the host, but being up front about that does not somehow make me interested.