One should not be accepted as a brahmana, kshatriya, vaishya, or shudra according to birth.

Herein it is clearly stated by Narada Muni that one should not be accepted as a brahmana, ksatriya, vaisya or sudra according to birth, for although this is going on now, it is not accepted by the sastras. As stated in Bhagavad-gita (4.13), catur-varnyam maya srstam guna-karma-vibhagasah. Thus the four divisions of society–brahmana, ksatriya, vaisya and sudra–are to be ascertained according to qualities and activities. If one was born in a brahmana family and has acquired the brahminical qualifications, he is to be accepted as a brahmana; otherwise, he should be considered a brahma-bandhu. Similarly, if a sudra acquires the qualities of a brahmana, although he was born in a sudra family, he is not a sudra; because he has developed the qualities of a brahmana, he should be accepted as a brahmana. The Krishna consciousness movement is meant to develop these brahminical qualities. Regardless of the community in which one was born, if one develops the qualities of a brahmana he should be accepted as a brahmana, and he then may be offered the order of sannyasa. Unless one is qualified in terms of the brahminical symptoms, one cannot take sannyasa. In designating a person a brahmana, ksatriya, vaisya or sudra, birth is not the essential symptom. This understanding is very important. Herein Narada Muni distinctly says that one may be accepted according to the caste of his birth if he has the corresponding qualifications, but otherwise he should not. One who has attained the qualifications of a brahmana, regardless of where he was born, should be accepted as a brahmana. Similarly, if one has developed the qualities of a sudra or a candala, regardless of where he was born, he should be accepted in terms of those symptoms.

Source: A.C. Bhaktivedanta Swami Prabhupada (2014 edition), “Srimad Bhagavatam”, Seventh Canto, Chapter 11 – Text 35