Goswamis

Chastity is such an important “regulative injunction” that Sanatana Goswami’s Hari-bhakti-vilasa states it as a Qualification to Receive Initiation, for a woman. One can infer that to be unchaste is a disqualification to receive initiation, and against the injunction of the Goswamis:

 “Hari-bhakti-vilasa 1.194, regarding mantra-adhikari,
the qualification for receiving mantra initiation:

tantrikeshu ca mantreshu dikshayam yoshitam api
sadhvinam adhikaro ‘sti sudradinam ca sad-dhiyam

“Sudras and women who are chaste and sincerely interested in understanding the
Absolute Truth are qualified to be initiated with the pancaratrika-mantras. 
This is
confirmed by Lord Krishna in the Bhagavad-gita 9.32” 
[HBV 1.194 as quoted in CC Madhya 24.331]

“Although we are initiating people from low-grade society, still, following the principles of Pancaratriki-vidhi, injunction of the Gosvamis. Therefore it is bona fide.”
[NOD Lecture, Vrindavana, October 27, 1972]

Jiva Goswami mentions women’s being “dear and kind to their husband” as a qualification to worship Lord Vishnu and states it is “eternal teaching of the Vedas”, clearly not something to be considered irrelevant nowadays:

“Women who are dear and kind to their husbands are also qualified to worship Lord Visnu.
This is the eternal teaching of the Vedas.” 
[Jiva Goswami Bhakti-sandarbha Anuccheda 298]

A guru gives diksa “according to the sastric principles”:

“A guru is a brahmana by qualification, and he can turn others into brahmanas according
to the sastric principles and brahminical qualifications.” [CC Madhya 16.186] 

Prabhupada refers to his CC ML 15.108 Purport for a detailed explanation of diksa:

“As far as dīkṣā is concerned, one should consult Madhya-līlā, Chapter Fifteen (108).”
[CC Madhya 24.331]

CC ML 15:108 elaborately explains diksa and quotes from Jiva Goswami’s Bhakti-sandarbha, Sanatana Goswami’s Hari-bhakti-vilasa, Tattva-sagara and the Agastya-samhita.

“The Hari-bhakti-vilāsa (17.11,12) in discussing the puraścaryā process, quotes the following verses from Agastya-saṁhitā:

“In the morning, afternoon and evening, one should worship the Deity, chant the Hare Kṛṣṇa mantra, offer oblations, perform a fire sacrifice, and feed the brāhmaṇas.

These five activities constitute puraścaryā. To attain full success when taking initiation from the spiritual master, one should first perform these puraścaryā processes.”

…In the Hari-bhakti-vilāsa (17.4,5,7) it is stated:

“Without performing the puraścaryā activities, one cannot become perfect even
by chanting this mantra for hundreds of years. However, one who has undergone the
puraścaryā-vidhi process can attain success very easily. If one wishes to perfect his initiation,
he must first undergo the puraścaryā activities. The puraścaryā process is the life-force by which one is successful in chanting the mantra. Without the life-force, one cannot do anything; similarly, without the life force of puraścaryā-vidhi, no mantra can be perfected.”

…The offenseless chanting of the holy name does not depend on the initiation process. Although initiation may depend on puraścaryā or puraścaraṇa, the actual chanting of the holy name does not depend on puraścaryā-vidhi, or the regulative principles. If one chants the holy name once without committing an offense, he attains all success.” 

Purascarya/purascarana is also known as panca samskara or five samskaras. Prabhupada instituted fire yajna as part of the diksa ceremony by the acarya, however a woman is forbidden to perform a fire yajna independently, as we have seen in Part One from Manu-samhita 5.155:

“No sacrifice, no vow, no fast must be performed by women apart (from their husbands).

“the wife is not authorized to do religious acts independently of her husband
or without his consent.”

A woman “is not qualified” to perform a fire yajna independently as a brahmana, which forms part of the diksa guru performing a bonafide initiation ceremony. A woman does not and cannot undergo “the sacred thread ceremony”; therefore she “is not qualified” to be a diksa guru, according to Srila Bhaktisiddhanta:

“if an initiated person has not undergone the sacred thread ceremony, he is not qualified
to be a guru; rather he is fit for rejection.” 
[Brahmana and Vaisnava p. 1989]