A:
Allah (Glorified and Exalted be He) orders children to be dutiful to their parents, even if they are non-Muslim. However, they should not obey them in disobedience to Allah; they should not love them (because they are disbelievers and Muslims can not love the disbelievers even if they are their relatives). Allah (Exalted be He) says,
And We have enjoined on man (to be dutiful and good) to his parents. His mother bore him in weakness and hardship upon weakness and hardship, and his weaning is in two years - give thanks to Me and to your parents. Unto Me is the final destination.
But if they (both) strive against you to make you join in worship with Me others that of which you have no knowledge, then obey them not; but behave with them in the world kindly, and follow the path of him who turns to Me in repentance and in obedience.
(Part No. 25; Page No. 279) Allah (Exalted be He) also says,
You (O Muhammad صلى الله عليه وسلم) will not find any people who believe in Allâh and the Last Day, making friendship with those who oppose Allâh and His Messenger (Muhammad صلى الله عليه وسلم), even though they were their fathers or their sons
A person should do good to his non-Muslim parents by supporting them if they are poor, kind treatment, and calling them to Islam. However, when they pass away, only their non-Muslim relatives inherit them for the Prophet (peace be upon him) said,
Neither a disbeliever inherits from a Muslim, nor a Muslim from a disbeliever.
May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.