If I had been in her shoes, I would have figured that in God's eyes, keeping the job while refusing on religious grounds to carry out certain tasks and leaving them to co-workers of less or no faith, would have been surrender.
Say you're a nurse in a doctor's office and assist him in all kinds of procedures to help heal people. Then he adds abortions to his out-patient services. Would you quit working for that doctor because you object to what is surely murder in the eyes of the Lord, or would you insist that when your boss the doctor performed abortions, he used another nurse to assist, but you'd remain to help in every other way for him to continue running a successful practice?
This woman put her money where her mouth is. Staying and declining to do certain work on the technicality of "refusal on religious grounds" would have been surrender.
Standing strong for righteousness is the ONLY way to achieve victory.
The thing is siince she is THE clerk and her signature is on that legal document. She is in effect endorsing the marriage. Read Romans 1:31-32.