The goal of Christians, in a culture of hypocrisy, isn't to add to that hypocrisy but to do their duty, live at peace, and do justly.
We can certainly acknowledge that there are clearly laws not being enforced under the current administration. This is wrong. Others, in contrast, appear to be over-enforced. Within it all, Christian ethics require that we obey the laws so long as they do not comprise a foundational Gospel issue and do not violate our personal being. Because Mrs Davis is an elected officer, her duty is to issue the licenses just like her deputy did today. If she cannot, and because this isn't a fundamental Gospel issue (no matter what certain fundamentalist leaders say,) her duty is to recuse herself from these duties or resign her office.
Martyrs aren't made by throwing themselves to the lions, and being placed in jail like this isn't martyrdom.