What is the authenticity of the hadith: "My flesh is from me, even if it be rotten," and can it be cited as evidence for those who are descendants of the Messenger of Allah, peace and blessings be upon him, but are engaged in acts of disobedience?

The mentioned Hadith has no basis. There is confusion in this matter between a person being from the Prophet's household (Ahl al-Bayt) and being among his awliya (allies/saints). While being attributed to the Ahl al-Bayt necessitates love, loyalty, and some specific rulings, the true alliance with the Messenger of Allah (peace be upon him) is achieved through piety and righteousness. Thus, every pious, righteous person is an ally of Allah and His Messenger, even if they are not from his household. As for someone who is from the Ahl al-Bayt but is corrupt in action, their kinship will not benefit them, for the Messenger of Allah (peace be upon him) said: "Indeed, my ally is Allah and the righteous believers." Moreover, mere lineage does not save a person on the Day of Resurrection, for "whoever is slowed down by his deeds will not be hastened by his lineage." The statement of those who claim to be from the Ahl al-Bayt that major sins do not harm them is false and contradicts explicit Islamic texts, such as the Quranic text that doubles the punishment for the Prophet's wives if they commit a clear immorality, and his (peace be upon him) saying to his daughter Fatimah: "O Fatimah, daughter of Muhammad, I cannot avail you anything against Allah." Ahl al-Sunnah love the Ahl al-Bayt, and the pious among them combine both virtues, while the disobedient among them still retain the original affection, but they are feared to incur Allah's punishment. For indeed, true alliance is for the pious.