yathā kāñcanatāṁ yāti kāṁsyaṁ rasa-vidhānataḥ tathā dīkṣā-vidhānena dvijatvaṁ jāyate nṛṇām

yatha kancanatam yati
kamsyam rasa-vidhanatah
tatha diksa-vidhanena
dvijatvam jayate nrnam
There is a difference between the smarta process and the gosvami process. According to the smarta process, one cannot be accepted as a brahmana unless he is born in a brahmana family. According to the gosvami process, the Hari-bhakti-vilasa and the Narada-pancaratra, anyone can be a brahmana if he is properly initiated by a bona fide spiritual master. This is also the verdict of Sukadeva Gosvami in Srimad-Bhagavatam (2.4.18):