Not a problem at all. If you follow the example of the AZ bill, one can also break a legal contract if it can be shown that the terms therein are against your religious principles. So… your rent or mortgage can be against your religion; as can utility bills; as can credit card payments; etc. I know I find all of these things highly offensive and pray daily that they will all go away!
But seriously, I worked at an ad agency in Boston in the mid-80s. One of our biggest clients was the Christian Science Monitor.
The paper, of course, has always been held in high esteem as a news organization — and a line of Cadbury cookies for which the client bought licensing rights (go figure) was a ton of fun to work on. But we also occasionally had to work on Church-related projects, like their so-called Nursing Guide
About that time, the sh¡t hit the media fan when a young boy died from an impacted bowel because his Christian Science parents refused to have him treated by medical doctors. Talk a/b squirm-worthy!
I was the lead art director on much of that business, and asked to be taken off of it as a matter of conscience. Management, in their compassion and understanding, took me off that account. And BASF. And Reebok. And Bank of Boston... 'Nudder words, I was sacked on the spot!
Yeah, some employers can't spell conscience, let alone have one.