Vaisnava is a vaisnava
Sri Caitanya-caritamrta
CC Antya-lila
A Vaiṣṇava is a Vaiṣṇava and should therefore be given all the respect due a Vaiṣṇava.
CC Antya 3.142, Purport: Stalwart, highly advanced Vaiṣṇava devotees are not interested in seeing prostitutes, but when a prostitute or any other fallen soul becomes a Vaiṣṇava, stalwart Vaiṣṇavas are interested in seeing them. Anyone can be turned into a Vaiṣṇava if he or she follows the Vaiṣṇava principles. A devotee who follows these principles is no longer on the material platform. Therefore, it is one’s strict adherence to the principles that should be considered, not the country of one’s birth. Many devotees join our Kṛṣṇa consciousness movement from Europe and America, but one should not therefore consider them European Vaiṣṇavas or American Vaiṣṇavas. A Vaiṣṇava is a Vaiṣṇava and should therefore be given all the respect due a Vaiṣṇava.