(Proverbs 6:20 KJV) My son, keep thy father's commandment, and forsake not the law of thy mother:
I may be looking for loopholes here but I think there is something that is understood but not stated. I believe it is assumed that the parents described here are people who are following the laws of God and are teaching what is found in the word.
There is a danger in loopholes. Too often we are looking for excuses to not do what we know is right. To often we are trying to make ourselves special cases. Our motives for obedience or rebellion can turn everything topsy turvy. The world is full of people who reject the God of the Bible but they still teach that murder is wrong.
So? Pay attention to the teaching of your parents but pay even more attention to the written word of God as a verification of what they have to say. That is a principle that applies to what you hear in school and from the pulpit also. You can never turn your thinking off.