Varṇāśrama is socially useful but spiritually secondary.
An example of this are the Traditional Parivāras.
Nityānanda Parivāra, Advaita Parivāra, Gadādhara Parivāra, Śrīvāsa (Paṇḍita) Parivāra, Narottama Dāsa Ṭhākura Parivāra, Śyāmānanda Parivāra, Śrīnivāsa Ācārya Parivāra, etc.
Why do Traditional Parivāras Still Use the Sacred Thread if Varṇāśrama is not important for Bhakti?
Traditional Gauḍīya Parivāras maintain the sacred thread because it serves a social and cultural function, not a spiritual one.
It is part of Hindu social life, not part of bhakti-sādhana.
No Parivāra claims that the sacred thread is required for chanting Kṛṣṇa’s name or attaining prema.
In other words, they maintain varṇāśrama as a social structure, not as a spiritual requirement.
This is exactly what Baladeva is saying:
for bhakti, varṇāśrama is irrelevant; for society, it may continue to exist.
In Iskcon and Gauḍīya Maṭha it is the same thing.
Varṇāśrama is socially useful but spiritually secondary.
The difference between the Traditional Parivāras and Iskcon Gauḍīya Maṭha is that the former emphasize Varṇāśrama by birth and the latter by quality.
But both emphasize Varṇāśrama as something socially useful and spiritually secondary.
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Baladeva Vidyābhūṣaṇa
Brahma-sūtra-kārikā-bhāṣya 3.4.36
Sūtra: antara capi tu tad-drsteh || ||
“Because scripture or experience shows this.”
Commentary: antarāyatayā kṛṣṇa-darśane bhaktasya vīkṣitāḥ |
śruti-varṇāśramācārāḥ || 36 ||
“The varṇāśrama practices prescribed in the śruti are regarded by the devotee as obstacles to the direct vision of Kṛṣṇa.”
Like everything in the Sastra, those who uphold Varnasrama along with the path of Bhakti will find a quote from the Sastra to support that view.
There is a statement that says: "Using the Sastra we can prove anything."
In any case, this quote from the Vedanta Sutra is very good.
Prabhupada felt that varnasrama was the best socio religious system. But he did not teach that it enhanced one's bhakti nor that failure to follow this marg would negatively impact one's bhakti. Why? Because that would be bhakti covered by karma, and Rupa Goswami advocated the sadhana of uttama bhakti, characterized marginally by not being covered by jnana of karma--jnana karmadi anavrtam.
As for brahmacari, grhasta, and sanyasa, these asrama orders have many duties associated with them within the varnasrama system that are not associated with bhakti and Prabhupafa did not institute them. He merely encouraged his disciples to practice uttama bhakti as celibate stdents, married couples, or renunciates.
That said, wherever the relative socio religious path of varnasrama does not depart from the absolute path of uttama bhakti it can be followed in a world where it is the socio religious system. We see this in the example of Mahaprabhu. But Prabhupada clearly said many times that varnasrama could not be established in our times, despite his preference for it as a socio religious system.
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The claim that “śāstra can prove anything” is usually a reaction to selective quotation without hermeneutics.
However, in Gauḍīya siddhānta, interpretation is governed by:
the authority of the Bhāgavata Purāṇa
the hermeneutical principles of Vedānta
systematic theology developed by the Gosvāmīs
Therefore, scripture cannot legitimately be used to prove anything, only conclusions that are consistent with the established siddhānta of bhakti.