A Vaisnava is already a brahmana; in fact, the highest stage of brahminical perfection is reached when one becomes a Vaisnava
SB Canto 3
Better than the brāhmaṇa who knows the purpose of the Vedas is he who can dissipate all doubts, and better than him is one who strictly follows the brahminical principles. Better than him is one who is liberated from all material contamination, and better than him is a pure devotee, who executes devotional service without expectation of reward.
Artha jña brāhmaṇa refers to one who has made a thorough analytical study of the Absolute Truth and who knows that the Absolute Truth is realized in three different phases, namely Brahman, Paramātmā and Bhagavān. If someone not only has this knowledge but is able to clear all doubts if questioned about the Absolute Truth, he is considered better. Further, there may be a learned brāhmaṇa-Vaiṣṇava who can explain clearly and eradicate all doubts, but if he does not follow the Vaiṣṇava principles, then he is not situated on a higher level. One must be able to clear all doubts and simultaneously be situated in the brahminical characteristics. Such a person, who knows the purpose of the Vedic injunctions, who can employ the principles laid down in the Vedic literatures and who teaches his disciples in that way, is called an ācārya. The position of an ācārya is that he executes devotional service with no desire for elevation to a higher position of life.
The highest perfectional brāhmaṇa is the Vaiṣṇava. A Vaiṣṇava who knows the science of the Absolute Truth but is not able to preach such knowledge to others is described as being in the lower stage, one who not only understands the principles of the science of God but can also preach is in the second stage, and one who not only can preach but who also sees everything in the Absolute Truth and the Absolute Truth in everything is in the highest class of Vaiṣṇavas. It is mentioned here that a Vaiṣṇava is already a brāhmaṇa; in fact, the highest stage of brahminical perfection is reached when one becomes a Vaiṣṇava.