It binds courts but does not have the power to write state laws. Kentucky can carve out religious exemptions for elected officials and citizens alike. Or they could get out of the marriage business altogether. Hauling this lady is nonsense and a reminder to any level headed American that the courts are no longer deserving of respect and without that courts are useless.
They could do either of those things but they haven't, and the Governor has said he sees no need to call the legislature into special session to deal with this situation because the Clerks in all but 2 or 3 of the state's counties have had no problem with issuing marriage licenses to same-sex couples.