There's a thread on Quora suggesting that Goloka is the cowshed of Kailasa as per Brahma Vaivarta Purana. Is this true?
Brahmavaivarta Purana is Krishna centric text. So there is no chance by at least 1000% that such a thing about Goloka (which Krishna followers consider as the Supreme realm) will be found in it.
However, this theory is found in the Shiva Purana, which is a 100% Shaiva sect text.
“O dear Viṣṇu, O Brahmā, cast off your fear from all sides. Certainly something good will result from the activities of Śaṅkhacūḍa.
I know all the details of his activities factually as well as those of Sudāmā the cowherd devotee of Kṛṣṇa.
At my bidding Viṣṇu has assumed the form of Kṛṣṇa and is stationed in the cowshed in the beautiful Goloka presided over by me.
Not according to BVP but According to Sro Shiva Purana.
Sri Shiva Purana 2.2:2:25.:
1-2. O Goddess, formerly once, Śiva, the creator supreme, called Viśvakarman to His highest region. He made him erect a large hall of great beauty in His cowshed, and an exquisite throne there.
3. Śiva, caused Viśvakarman to make an excellent, divine, wonderful umbrella for warding off obstacles.
4-5. He invited Indra and other gods, the Siddhas, Gandharvas, Nāgas, Upadeśas and Āgamas, Brahmā with his sons, the sages and the celestial goddesses and nymphs who came there with various articles.
6. Sixteen virgins each of devas, sages, Siddhas and serpents were brought for the auspicious ceremony.
7. O sages, different musical instruments like lutes, tabours etc. were played and songs sung. Thus there was great pomp and ceremony.
8. Articles necessary for a coronation including herbs were brought. Five pots were filled with the sacred waters from all flowing holy rivers.
9. All other divine arrangements were made by His attendants. Śiva caused them to recite Vedic mantras loudly.
10. With a delightful mind He called Viṣṇu from Vaikuṇṭha. O Goddess, Śiva rejoiced at the perfect devotion of Viṣṇu.
11. In an auspicious hour, the great lord made Viṣṇu sit on the exquisite throne and delightedly decorated him in every way.
12. A beautiful coronet was fixed on Viṣṇu and the auspicious holy thread was tied to his waist. He was then coronated by lord Śiva in the Cosmic Hall.
13. What was His own and even non-transferable, Śiva the independent and favourably disposed to His devotees, conferred on Viṣṇu and eulogised him.
14. The lord who is favourably disposed to His devotees, revealing Himself independent but subservient to the boons granted by Him, spoke these words to Brahmā the creator of all worlds.
Lord Śiva said:—
15-16. Lord, may you all hear. From now onwards, at my bidding, this Viṣṇu has become worthy of my respect and that of all devas. Dear one, you too bow to him. May all the Vedas extol him at my bidding as they extol me.
17. So saying, Rudra, Himself bowed to Garuḍa-bannered Viṣṇu. The bestower of boons, He who is favourably disposed to His devotees, felt delighted by his devotion to Viṣṇu.
18. Then Viṣṇu was duly revered by Brahmā followed by devas, sages, Siddhas and others.
19. Then the delighted Lord Śiva, favourably disposed towards his devotees, bestowed great boons on Viṣṇu and the other devas.
Lord Śiva said:—
20. At my bidding you are now the creator, sustainer and destroyer of all the worlds. You are the bestower of virtue, wealth and love and the chastiser of people of evil predilection.
21. You are the lord of the universe. You are worthy of the worship of the universe. You will be invincible in battle anywhere even against me (Same boon given to Sage Narayana). You will be endowed with great strength and valour.
22. You take three Śaktis—will etc. conferred by me. You can have the power of exhibiting diverse sports and independence in the three worlds.
23. O Viṣṇu, persons who hate you shall indeed be chastised and curbed by me with strenuous efforts. Salvation shall be given by me, O Viṣṇu, to your devotees.
24. Accept this Māyā too which cannot be withstood by devas and others and by which the entire universe will be deluded and made insentient as it were.
25. O Viṣṇu, you are my left hand, as Brahmā is my right hand. You shall be his progenitor and sustainer too.
26. Undoubtedly I myself am Rudra who is my heart. He is worthy of your respect as well as that of Brahmā and others too, of course.
27. While stationed here you protect the entire universe taking different incarnations and diverse ways of protection.
28. This place of great prosperity and glory in my own world shall be famous as Goloka. It will be very brilliant.
29. O Viṣṇu, I shall certainly see the various incarnations of yours on the earth and shall be delighted by your devotion to me.
30. After conferring thus unlimited prosperity on Viṣṇu, Śiva, the consort of Śivā, freely sported about at Kailāsa along with His attendants.
31. Thenceforth lord of Lakṣmī assumed the guise of a cowherd. The lord of cowherds, cowherdesses and the cows wandered there with pleasure.
32. The delightful Viṣṇu protected the universe taking up various incarnations and sustaining it at the bidding of Siva.
33. Now He has taken a fourfold incarnation at the bidding of Śiva. I who am Rāma, and my brothers Bharata, Lakṣmaṇa and Śatrughna are His incarnations.
Sri Shiva Maha Purana 2.5:5:31.:
1. On hearing these words of the distressed Viṣṇu and Brahmā, Śiva laughingly spoke in the rumbling tone of the cloud.
2. “O dear Viṣṇu, O Brahmā, cast off your fear from all sides. Certainly something good will result from the activities of Śaṅkhacūḍa.
3. I know all the details of his activities factually as well as those of Sudāmā the cowherd devotee of Kṛṣṇa.
4. At my bidding Viṣṇu has assumed the form of Kṛṣṇa and is stationed in the cowshed in the beautiful Goloka presided over by me.
5. Considering himself independent under a delusion he indulged in many kinds of sportive dalliance like a deluded licentious person.
6. On seeing his excessive delusion as a result of my deceptive art I suppressed their virtuous intellect and made them suffer curse.
7. Having thus performed my sport, I suppressed the illusion. Regaining knowledge they got rid of delusion and became well-intentioned.
8. They came near me in a piteous plight. After bowing to me they eulogised me devoutly and humbly with palms joined in reverence.
9. Overwhelmed by shame they told me all the details. Dejected, they lamented before me saying the words “Save us, O save us.”
10. Then I, becoming delighted, told them these words, Kṛṣṇa, you forget your fear at my behest.
11. I am the protector, always infused with love. Good will befall you. All this has happened at my will. There is no doubt in it.
12. Go to your abode along with Rādhā and your comrade. He will become a Dānava here in Bhārata, certainly.
13-14. At the proper time I shall redeem you from the curse”. What I told thus Śrīkṛṣṇa and Rādhā accepted readily. Śrīkṛṣṇa the intelligent rejoiced and returned to his abode. There they engaged themselves in propitiating me and bidding their time.
15. Realising that everything is subject to my control and his will is not independent, Sudāmā became the lord of Dānavas as a result of the curse of Rādhā.
16. The virtuous demon Śaṅkhacūḍa distresses and harasses the gods always with his might. He is evil-minded to this extent.
17. He has been deluded by my deception and hence he seeks the help of evil ministers. But myself being the chastiser of the wicked you can get rid of his fear quickly”.
I hope this clarifies all your queries. Prd..