Brahmavaivarta Purāṇa (4.115.112b-113a) mentions 5 kaliyuganiṣiddha karmas -
aśvamedham gavālabbhaṁ saṁnyāsaṁ palapaitr̥kam //
devareṇa sutotpati kalau pañca vivarjayet /
Saṁnyāsa is also mentioned under the Kaliyuga niṣiddhas, which is pretty strange. We clearly know that saṁnyāsa is present in Kaliyuga, and great śiṣṭa ācāryas such as Rāmānuja, Madhva, Śaṅkara Bhagavatapāda, etc. took saṁnyāsa. So, clearly this isn't a prohibition of saṁnyāsa, as a whole.
It's most likely a prohibition of a specific kind of saṁnyāsa. Some online articles by Gauḍīyas
(such as a
; b) in recent times, take the saṁnyāśa in above quoted śloka to mean karmasaṁnyāsa.
As per Kūrma Purāṇa (1.2.80), the bhikṣu who does relentless yogābhyāsa, remains steady on mokṣamārga, conquers over indriyas, and perseveres for attainment of jñāna, is 'pārameṣṭhika'.
Śloka (82) mentions three kinds of pārameṣṭhika, viz. jñānasaṁnyāsin, vedasaṁnyāsin, & karmasaṁnyāsin.
But the succeeding ślokas don't explain three saṁnyāsins.
yogābhāsarato nityamārurukṣurjitendriyaḥ /
jñānāya vartate bhikṣuḥ procyate pārameṣṭhikaḥ // (80)
jñānasaṁnyāsinaḥ kecidvedasaṁnyāsino'pare /
karmasaṁnyāsinaḥ kecit trividhāḥ pārameṣṭhikāḥ // (82)
As per 'common' usage of karmasaṁnyāsa, we know that it refers to karmayoga, propounded by Kr̥ṣṇa, in Bhagavad Gītā. So, that karma saṁnyāsa isn't a niṣiddha kriyā for Kaliyuga. Nāradaparivrājakopaniṣat (5.6) gives a def. of karmasaṁnyāsin. Karmasaṁnyāsin is the person (even if he has abhāva of vairāgya), who takes saṁnyāsa, after living through first three āśramas (brahmacarya, gr̥hastha, & vānaprastha).
brahmacaryaṁ samāpya gr̥hī bhūtvā vānaprasthāśramametya vairāgyabhāve'pyāśramakramānusāreṇa yaḥ saṁnyasyati sa karmasaṁnyāsī //
So, perhaps this is the kind of saṁnyāsa, which Gauḍīyas are referring to. Unfortunately, they don't provide any śāstriya support afaik, for taking this stance.
But there is an observation, we can work with, that is the lack of vānaprasthīs, since more than a 100 yrs. We don't see anyone taking vānaprastha āśrama. People usually go directly to saṁnyāsa āśrama after gr̥hastha or brahmacarya, but are rarely seen taking karmasaṁnyāsa (as defined in Nāradaparivrājakopaniṣat).
Is vānaprastha niṣiddha in Kaliyuga?
The famous dharmanibandha 'Dharmasindhu' by Kāśīnātha Upādhyāya (1 ; 2 ; 3), also mentions the niṣiddhakarmas (>5) for Kaliyuga, and these are as follows:
samudrayātrā (for dvijas), bearing kamaṇḍalu (to misdirect public),
dvija having vivāha with those of other varṇas, niyoga with devara,
paśubali at madhuparka, offering & bhakṣaṇa of māṁsa at śrāddha,
entering vānaprastha āśrama, re-kanyā-dāna of one's kanyā (who's
akṣatyoni) to someone else, being in brahmacarya for too long
(dīrgha-kālaṁ), naramedha, aśvamedha, mahāprasthāna, gomedha, doing
prāyaścitta of mahāpāpa that culminates in death, madyapāna (including
that in yajñas such sautrāmaṇi, etc.), following the śāstras of
vāmācāra on the issue of madyapāna, etc. (because madyapāna, etc. is
prohibited by śiṣṭas in both Pūrva & Uttara Mīmāṁsā), having putras
other than aurasa or dattaka/kanīna (there are 12 kinds of sons, as
per śāśtras, and 10 of these are niṣiddha in Kaliyuga. But, as per
Kaustubha grantha, apart from aurasa & kanīna, svayaṁdatta/sahoḍhaja
is also yogya in Kaliyuga, and the rest of 9 kinds of sons are
niṣiddha), and removing a person from deśa, grāma, kula or jāti upon
their committing mahāpāpa (such as Brahmahatyā), etc.
Since, vānaprastha comes under kalivarjya, so karmasaṁnyāsa (as defined in Nāradaparivrājakopaniṣat) is automatically also a Kaliyuga niṣiddhakarma.