Is a judge who rules according to state laws that contradict the Sharia of Allah sinful, or does the sin lie with the state? And is a judge who rules with such judgments considered an apostate, outside the fold of Islam?

It is not permissible for a Muslim to rule by other than what Allah has revealed, whether on his own initiative or by order of the state, because there is no obedience to a creature in disobedience to the Creator. As for working in the judiciary profession within man-made systems for those who confine themselves to cases that do not contradict the Sharia (definition), some scholars have permitted it, especially for those who are able to reduce injustice, spread justice, and avoid what contradicts the Sharia. The ruling on judging by other than what Allah has revealed varies between major disbelief and lesser forms, depending on the circumstances.