Many a times I have heard that question. And I think many people misunderstand the official stance of Iskcon on that question. Srila Prabhupada has often used to say to his disciples that in public they should never present their organisation and themselves as a Hindu. And because of that many people misunderstood that thing to mean that Srila Prabhupada refused to identify his Iskcon movement to be a Hindu organisation.
Srila Prabhupada said:
Hindu dharma is a vague term. Real dharma is varṇāśrama-dharma. Hindu dharma we don't find, any Vedic literature. Neither in the Bhagavad-gītā. It is a, a nomenclature given by the Muhammadans---"Hindus." From Sindhu, "Hindu." Anyway, now we are known as Hindus.
It's not that he did not recognise Iskcon as a Hindu, but he just wanted his movement and disciples to specify that they are Lord Krishna's people.
Srila Prabhupada said:
Prabhupāda: No, we are clearly stating "Kṛṣṇa consciousness."
Srila Prabhupada said:
They are attracted to Kṛṣṇa. These people, they are [Hindi]. But you are taking Kṛṣṇa as Hindu. That is your mistake. Kṛṣṇa is... Hindu ne. He is God. He is God. God Hindu ne, Mussulman ne, Christian ne, Parsi ne—God is God. [Hindi] And I am also not interested to preach Hindu dharma. [Hindi] ...Kṛṣṇa dharma. Kṛṣṇa consciousness, that is the only dharma. [Hindi] ...Kṛṣṇa literature. It is not a Hindu dharma literature. [Hindi]
So they are not interested in many gods, Durga, Kali, or Śiva, or... [Hindi] Strictly, if you take the version of Bhagavad-gītā, why Bhagavān says that "You give up all religion. Simply you take to the shelter of My feet?" That means to take shelter of Kṛṣṇa's lotus feet is the only religion.
He just wanted his movement and disciples to be recognised as Lord Krishna's people specifically, and not as Hindus which is one broad, unspecified and vague term.
This: "to take shelter of Kṛṣṇa's lotus feet is the only religion" -- to take shelter solely in Krishna is the only religion for Srila Prabhupada.
He is quoting a verse from the Bhagavad-gita 18.66:
Abandon all varieties of religion and just surrender unto Me. I shall deliver you from all sinful reactions. Do not fear.
In the above speech he translated that verse a bit different: "You give up all religion. Simply you take to the shelter of My feet".
So a Vaishnava should not be interested in other gods, Indra, Agni, Surya, Shiva, Durga, etc, and Gaudiya Vaishnavas even think that there is no need to be interested in other forms of Lord Vishnu such as Lakshmi-Narayana, Sita-Rama, etc, but only in Radha-Krishna!