If a person born in the family of a brahmana is void of brahminical qualification, then he must be treated as a non-brahmana or, in better terms, a relative of a brahmana

Expressions researched:
"similarly if a person born in the family of a brāhmaṇa is void of brahminical qualification, then he must be treated as a non-brāhmaṇa or, in better terms, a relative of a brāhmaṇa"

Srimad-Bhagavatam

SB Canto 1

The śāstra enjoins that even if good qualifications are seen in a person born in a family other than that of a brāhmaṇa, the qualified man has to be accepted as a brāhmaṇa, and similarly if a person born in the family of a brāhmaṇa is void of brahminical qualification, then he must be treated as a non-brāhmaṇa or, in better terms, a relative of a brāhmaṇa.

SB 1.7.35, Translation and Purport

Lord Śrī Kṛṣṇa said: O Arjuna, you should not show mercy by releasing this relative of a brāhmaṇa [brahma-bandhu], for he has killed innocent boys in their sleep.

The word brahma-bandhu is significant. A person who happens to take birth in the family of a brāhmaṇa but is not qualified to be called a brāhmaṇa is addressed as the relative of a brāhmaṇa, and not as a brāhmaṇa. The son of a high-court judge is not virtually a high-court judge, but there is no harm in addressing a high-court judge's son as a relative of the Honorable Justice. Therefore, as by birth only one does not become a high-court judge, so also one does not become a brāhmaṇa simply by birthright but by acquiring the necessary qualifications of a brāhmaṇa. As the high-court judgeship is a post for the qualified man, so also the post of a brāhmaṇa is attainable by qualification only. The śāstra enjoins that even if good qualifications are seen in a person born in a family other than that of a brāhmaṇa, the qualified man has to be accepted as a brāhmaṇa, and similarly if a person born in the family of a brāhmaṇa is void of brahminical qualification, then he must be treated as a non-brāhmaṇa or, in better terms, a relative of a brāhmaṇa. Lord Śrī Kṛṣṇa, the supreme authority of all religious principles, the Vedas, has personally pointed out these differences, and He is about to explain the reason for this in the following ślokas.