I believe he had the option of fining her instead of jailing her once she was found in contempt. But in looking further into it, he saw there was no shortage of religious supremist whackos stepping forward to give her all kinds of money. So she would be able to continue to pay her fines and impose her religious will on others and not do her elected job. So, while surprising to some as extreme, he jailed her. Then I think he kind of ignored the law and looked for a solution to the original problem: Can we get marriage licenses to the people in this county? When the answer was yes, he let her go.
I find a similarity although without the direct governmental employee angle to employers who provide healthcare to employees as part of their benefits package. Yet somehow, some are able to refuse to allow birth control or abortions as part of that package.
No, healthcare is part of what you agreed to pay me to do the job you want me to do. You have 0 right to personally wade into my healthcare decisions and impose your personal religious will on me.
Look for the Helpers. You will always find people who are helping.
-Mr. Rogers' Mom