The basic problem here is should a Christian government official uphold an immoral law or not. This lady has shown courage standing up for her conviction that an immoral law does not hold the power of law and claims the authority of God to oppose the Supreme Court. So the authorities in your country(since they do not recognise Gods authority over civic laws) have dismissed her from her post and imprisoned her. They have claimed that she was simply refusing to do her job but since she has been doing this job for a while now the real reason she is in jail is the opposition to gay marriage. What they could have done is delegate the power to marry gays to a willing member of the office. Afterall the legal document is endorsed by the office not the individual. But there seems to be no provision for religious objection in the current rules beyond dismissal. Personally i think a change in the rules to accomodate religious objection is a better alternative to denuding government of all Christian officials.
Her imprisonment undermines the rule of law per see because she has not done anything wrong. Let the state give out its pieces of paper to gay couples if it wants but do not force Christians or Muslims who object to this to do the handing out. Gay "marriages" are afterall a small % of business in this area.
You would not force Muslims to sell alcohol or Jews pork so why force this?
Follow along closely and I will explain in simple terms.
If a Muslim decides to work in an environment that sells alcohol, the employer may accommodate them to not have to sell it, but when a customer walks in the store to buy alcohol, someone else in that store will sell it to them.
If the Jew decides to work in an environment that sells pork, the employer may accommodate them so they don't have to directly sell the pork, but when a customer walks in the store that sells pork to buy some, someone else will indeed sell it to them.
In essence, the business and or government agency, can not be held hostage because of the personal faith beliefs of one person, because the business needs to serve their customers.
Kim Davis, was given the opportunity to not have to issue the licenses herself and to have other people do so, but she said she would not let that happen and she would interfere with others in the office issuing the licenses. So, what Kim Davis was doing, was holding the entire clerks office hostage, from being able to issue legal marriage licenses and even with the fact, she took an oath to uphold the law.
This would be the equivalent, of the jew telling his employer, they can not sell pork to anyone and the Muslim telling their employer, they can not sell alcohol to anyone and if they even try, they will do everything in their power, to stop it.
Hope this bit of reality, clears things up a bit.