Is a young man considered disobedient to his parents if he disobeys their command not to mix with his brothers from the mosque, or visit them, or borrow books from them, knowing that this affects his spiritual progress, despite his attempts to convince them of the good character of the people of the mosque?

You must treat your parents with wisdom and kindness, and know that they have a right over you that does not cease, even if they are polytheists. As Allah the Almighty commanded in the noble verse: "And We have enjoined upon man [care] for his parents. His mother carried him through hardships upon hardships, and his weaning is in two years. Be grateful to Me and to your parents; to Me is the [final] destination. But if they endeavor to make you associate with Me that of which you have no knowledge, do not obey them, but accompany them in [this] world with appropriate kindness and follow the way of those who turn back to Me." So, accompany them with kindness, and supplicate to Allah to open their hearts to the truth. Try to convince them of the correctness of your righteous path, and explain to them the good that will result from your righteousness for them in this world and the Hereafter, citing the Hadith of the Prophet, peace and blessings be upon him: "When a person dies, his deeds are cut off except for three: a continuous charity, knowledge from which benefit is derived, or a righteous child who prays for him."