Birth in the Lord’s family or in the Acharya’s family cannot constitute the qualification for a respectable person.

“Every living being is part and parcel of the Supreme Lord, as stated in the Bhagavad-gītā (mamaivāṁśaḥ). Every living entity is originally a son of God, yet to execute His pastimes the Lord selects certain highly qualified living entities whom He allows to take birth as His personal relatives. But those living entities who appear as descendants of the Lord’s personal family may undoubtedly become proud of such a position and thus abuse the great adulation they receive from ordinary people. In this way such persons may artificially get undue attention and divert people from the actual principle of spiritual advancement, which is to surrender to the pure devotee who represents the Lord. Ordinary people, however, not understanding the higher principles of spiritual knowledge, easily forget the actual qualifications of a bona fide spiritual master and instead give undue importance to people born in the Lord’s so-called family. Śrī Caitanya Mahāprabhu, therefore, avoided this impediment on the path of spiritual enlightenment by leaving behind no children. Although Caitanya Mahāprabhu married twice, He was childless. Nityānanda Prabhu, who is also the Supreme Personality of Godhead, did not accept any of the natural sons born of His own son, Śrī Vīrabhadra.
“In the Middle Ages, after the disappearance of Lord Caitanya’s great associate Lord Nityānanda, a class of priestly persons claimed to be the descendants of Nityānanda, calling themselves the gosvāmī caste. They further claimed that the practice and spreading of devotional service belonged only to their particular class, which was known as nityānanda-vaṁśa. In this way they exercised their artificial power for some time, until Śrīla Bhaktisiddhānta Sarasvatī Ṭhākura, the powerful ācārya of the Gauḍīya Vaiṣṇava sampradāya, completely smashed their idea. There was a great hard struggle for some time, but it has turned out successful, and it is now correctly and practically established that devotional service is not restricted to a particular class of men. Besides that, anyone who is engaged in devotional service is already a high-class brāhmaṇa. So Śrīla Bhaktisiddhānta Sarasvatī Ṭhākura’s struggle for this movement has come out successful. It is on the basis of his position that anyone, from any part of the universe, can become a Gauḍīya Vaiṣṇava.”

In other words, the essence of spiritual knowledge is that every living being, regardless of his present status in life, is originally a servant of the Supreme Lord, and it is the mission of the Lord to reclaim all of these fallen living entities. Despite his past situation, any living being who is willing to surrender again at the lotus feet of the Supreme Lord or His bona fide representative can purify himself by strictly adhering to the rules and regulations of bhakti-yoga and thus act as a high-class brāhmaṇa. Nonetheless, the seminal descendants of the Lord think themselves to have acquired their ancestor’s character and position. Thus the Supreme Lord, who is the well-wisher of the entire universe and especially of His devotees, bewilders the discriminatory power of His own descendants in such a contradictory way that these seminal descendants become recognized as deviant and the actual qualification to be a representative of the Lord, namely unalloyed surrender to the will of Kṛṣṇa, remains prominent.”

Source: A.C. Bhaktivedanta Swami Prabhupada (2014 edition), “Srimad Bhagavatam”, Eleventh Canto, Chapter 01 – Text 05.