How can the son's desire to go to the mosque to memorize the Qur'an be reconciled with his parents' fear of him being subjected to security harassment, especially since the father associates memorizing the Qur'an with extremism?

The rights of parents are great, and being dutiful to them is obligatory. However, it is not permissible to obey them in matters that contradict obedience to Allah, for the Prophet, peace and blessings be upon him, said: "Obedience is only in what is good," and "Listening and obeying are incumbent upon a Muslim individual in what he likes and dislikes, as long as he is not commanded to commit an act of disobedience. If he is commanded to commit an act of disobedience, then there is no listening and no obeying," and "There is no obedience to a creature in disobedience to the Creator." If you fear eyes that follow worshipers and harm them, then that is an excuse that permits absence from the congregational prayer, provided that the fear is valid and based on existing reasons, not mere delusions.