All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
This supplication, known as "Hizb al-Nawawi," is indeed attributed to Imam al-Nawawi, and it is part of the adhkar (remembrances) that have been associated with him. Imam al-Sakhawi mentioned it in his book {Al-Manhal al-Azab al-Rawi fi Tarjamat Qutb al-Awliya al-Nawawi, Page 9}. Scholars and righteous individuals have accepted and practiced it from the time of Imam al-Nawawi until our present day. They have written numerous explanations and commentaries on it. Contemporary scholars and hadith experts also transmit it with a connected chain of narration back to Imam al-Nawawi, may Allah have mercy on him.
The Hizb al-Imam al-Nawawi includes supplications and remembrances that Muslims recite in the morning and evening. It is believed by many to be a means of protection from various spiritual and worldly harms, such as magic, the evil eye, envy, Satan, worries, and anxieties, by the permission of Allah, the Most High.
Regarding the meaning of Imam al-Nawawi's statement (and upon their religions), it refers to their acts of obedience, worship, and acts of devotion. The term "أديان" (religions) in the Arabic language can encompass several meanings, including reward, obedience, judgment, and accountability. Ibn Fares, a notable linguist, explained it as follows: "As for His saying, exalted is He, He could not take his brother by the law of the king' [Yusuf: 76], it can be said to mean 'in his obedience,' or 'in his judgment.' And from it: 'مالك يوم الدين' [Al-Fatiha: 4], meaning the Day of Judgment. Some people say it refers to accountability and recompense. Whatever it may be, it is a matter to which one submits." {Mo`jam Maqayyees Al-Lughah, Vol.2, Page 320}.
The pronoun "هم" (their) refers to one's family, children, and companions. The intended meaning is a supplication to Allah, asking Him to safeguard the acts of obedience of one's family, children, and companions, protecting them from the whispers and schemes of both human and jinn devils and from being lured into doubtful matters and forbidden desires.
Therefore, this Hizb attributed to Shaykh al-Islam Imam al-Nawawi, may Allah have mercy on him, has been transmitted through a connected chain of narration by scholars, and its blessings become evident for those who consistently recite it. Preserving it is akin to the preservation of the remembrance of Allah, which is one of the greatest acts of worship. The term "أديانهم" (their religions) in this context primarily refers to acts of obedience. And Allah the Almighty knows best.