This is completely off topic, because as has been pointed out before, the mother in this case is having her legal rights trampled, while Kim Davis was trampling other people’s legal rights.
However…
No. Davis put herself into that job, as an elected official. No one needs to “find her a new job” - she either carries out the job that she actively campaigned to do, and stops preventing her charges from carrying out their job, or she removes herself from the position she was elected into, which she feels she can no longer perform to its full requirements.
Doing either of those things would be for her to “do her damn job”, and if she absolutely refused to acknowledge the legal rights of the citizens due to her religion then the correct thing to do would be the second option. But instead she actively used her position to deny legal rights to the citizens she swore to serve, while refusing to remove herself from the job she swore to do.
The Constitution did not change. And if she feels she can’t uphold the government’s laws, she should not be a government official. She can make as much of a stink about it as she wants, but she can’t do so while hypocritically remaining in that position.
You gave an example before:
Know what they did differently from Kim Davis? They removed themselves from the job they were objecting to. A more accurate comparison with Davis would be a soldier who decided to become an active saboteur rather than just refusing orders.