Answer
Srila Prabhupada makes this statement because he is simply repeating the teachings of the scriptures.
The scriptures declare that regardless of one's background—whether one is born in a cultured family, a sinful family, or has been associated with people engaged in sinful activities—anyone can become completely purified by taking shelter of a pure devotee and sincerely practicing Krishna consciousness under the guidance of the spiritual master.
This is not merely a theoretical statement; it has been repeatedly demonstrated throughout history.
Srila Prabhupada himself proved this when he first went to America. Many of the people who came to him were hippies and were deeply accustomed to various sinful habits. Yet, Prabhupada did not reject them.
Instead, he patiently guided them to begin practicing Krishna consciousness by chanting the Hare Krishna maha-mantra, honoring Krishna prasadam, and following the regulative principles. Gradually, they became purified and developed into sincere Vaishnavas.
The scriptures also provide many examples.
One famous example is the story of Mṛgāri, the hunter who met Narada Muni. Mṛgāri was extraordinarily cruel. He not only killed animals but deliberately wounded them and left them half-dead, taking pleasure in watching them suffer.
Yet, by the association and instructions of Narada Muni, he completely gave up his sinful occupation, began chanting the holy name of the Lord, and in a short time became a pure devotee.
Another well-known example is Ajamila.
Ajamila was born in a pious brahmana family and received proper spiritual training in his youth. However, after associating with a person of sinful character, he abandoned his righteous life and became deeply engaged in sinful activities.
Despite this, at the end of his life he called out the name "Narayana." Although he was calling his youngest son, whose name was Narayana, he nevertheless uttered the holy name of the Lord. As a result, he became purified, later took up devotional service properly, became a pure devotee, and ultimately returned to Godhead.
The Srimad-Bhagavatam repeatedly declares that simply by chanting the holy names of the Lord, even the most sinful person can become completely purified of all sinful reactions.
The scriptures further explain that chanting the Hare Krishna maha-mantra is the highest and most effective form of atonement for all sinful activities. It not only frees one from sinful reactions and hellish consequences but also awakens pure devotion to Krishna.
Therefore, Srila Prabhupada confidently states that anyone can become a pure Vaishnava—not because of personal opinion, but because this is the verdict of the scriptures, confirmed by the examples of great devotees and demonstrated practically through his own preaching mission.
Anyone who sincerely follows the instructions of a pure devotee and practices Krishna consciousness can become fully purified and attain pure devotional service.
