Is it permissible to seek forgiveness and recite Al-Fatihah for deceased Christian parents? What are their rights over a Muslim after their death, and how can one show them piety?

It is not permissible to seek forgiveness for polytheists (mushrikin) or to recite Al-Fatihah for them, due to the Almighty's saying: "It is not for the Prophet and those who have believed to ask forgiveness for polytheists, even if they were relatives, after it has become clear to them that they are companions of Hellfire." The Prophet (peace be upon him) sought permission from his Lord to ask forgiveness for his mother, but he was not granted permission, and Allah said: "Indeed, my father and your father are in the Fire." So, whoever dies upon disbelief is in the Fire, and the kinship of close relatives will not benefit them.

As for honoring disbelieving parents after their death, it is done by settling their debts, fulfilling their covenants in matters that are not forbidden, maintaining the ties of kinship that can only be maintained through them, and honoring their friends, without showing allegiance if the friend is a disbeliever.