What is the governing principle for the Hadith: "There is no obedience to a creature in disobedience to the Creator" when it comes to parents in matters of dispute? And is their obedience obligatory in permissible matters, and what are the rules and guidelines that can be relied upon in that regard?

Obeying one's parents is obligatory in permissible matters if there is benefit for them and no harm to the child, and in doubtful matters. As for disputed issues, it is not permissible to obey them if the child believes that what they commanded is forbidden or that the opposite is obligatory, because "there is no obedience to a creature in disobedience to the Creator." However, one must be gentle in responding and show love and respect.