Is it permissible to practice the professions of judging and lawyering, knowing that they operate according to man-made laws?

It is not permissible to work in the profession of judging unless the ruling continues according to God's law; otherwise, it is severely forbidden. As for working in the legal profession, if it is for documenting contracts, then there is no harm. However, if it is for defense or prosecution, it is not permissible unless it is conditioned upon not assisting the oppressor in his oppression.