Short answer:
There is NO old portrait in Kanchi math depicting Adi Shankara wearing a yajnopavita. Where is a link to that portrait? There are some portraits of Shankara wearing yajnopavita and no danda and wearing white dhoti. These are his pre-sannyas days.
Show the portrait in Kanchi math. This should include danda, wearing ochre robes but having yajnopavita. Nothing like that exists. Please note this should actually link to the kamakoti site and not some twitter account.
You should read the Chapter 5 of the book A History of the Dasnami Naga Sannyasis available in google books. It clearly describes the rituals involved that includes pinda dana to ancestors. This is given below. Please see my main point taken from Jivan mukti viveka to answer some questions raised by you in the comments. If you want a youtube version of the rituals they are followed, please see the initiation of sri vidhusekhara bharati, the junior pontiff of the Sringeri math.
Long answer:
The Dashnami Sampradaya and the sri vaishnava sampradhaya follow entirely different texts on the sannyasa dharma.
The Yatilingasamarthana of Vatsya Varadacharya describes in detail the characteristics, qualifications and duties of Srivaishnava ascetics.
Tridandam vainavam soumyam satvacham samaparvakam | Veshtitham
krishnagovaaLarajjvaa tu chaturanguhm ||
‘An ascetic should take three staves of bamboo and tie them together
with a rope made of the hair of the cow’s tail, four angulas in
length.’
Vaag dando atha manodandah kaayadandas tathaiva cha | Yasyaithe
nihitaa buddhau tridanditi cha uchyate ||
‘A Sannyasi should always possess the following five things;
yajnopavita (sacred thread), tridanda (holy staff), jalapavitra
kaupina and kati vastra (the covering cloth)’.
According to srivaishnava tradition of Ramanuja, a brAhmaNa, even after becoming
a sannyAsi, retains many of the duties that are incumbent on his being a brAhmaNa. This is why sannyasis of this order retain their sacred thread (yajnOpavIta)
and tuft of hair (SikhA). They must continue to do their sandhyAvandana and gAyatrI japa at the appointed times. Whatever rituals were practiced in the purva ashrama should be continued. Even looking at a sannyasi who has removed the yagnopavita and shikha results in impurity and one should take bath after this. This includes looking at jivan muktas such as Kanchi periya or Sringeri mathadipadis.
Rules and Regulations of Brahmanical Asceticism: Yatidharmasamuccaya of Yadava Prakasa gives the details of various sannyasa as existed in the 13th century and what is followed currently by Sri Vaishnavas.
However, there are lots of texts that indicate the removal of tuft of hair and yagnopita is required for sannyas ashram. The concept of removing the tuft and sacred thread is given in many upanishads and puranas.
The seeker, holding one staff, gives up along with the sacred thread
the topknot; but when the supreme Brahman is realized directly and
immediately, giving up everything the ascetic, going out, becomes a
mendicant’ (Narada P. Up. 3.17).
The Parabrahma Upanishad primarily describes why the sacred thread and topknot hair tuft are abandoned by Sannyasi as that knowledge is the inner sacrificial string of the renouncers, and knowledge is their topknot. See the book.
Please check out the book, A History of the Dasnami Naga Sannyasis edited by Ananda Bhattacharyya. The Chapter 5 of the book titled rules and practices of Dasnami monks clearly entails the procedure for becoming a monk and also the practices to be followed. There are many scriptures that are followed as the basis for this practice. The primary is the yagnavalkya smriti. The compilation of these rules and regulations and their basis can be found in the sannyas-grahan paddhati. Yati dharma Sangrah of Visweshwara Saraswati gives further details of the sannyas tradition.
He goes through many ceremonies which are described fully below, on
the authority of the 'Sannyas-Grahan Paudhati' of Paramhansa
Gopalanand (Benares, 1998) and the Yatidharma Sangraha of Visheshwar
Saraswati (Anand Ashram Press, 1909).
On the following day, he should bathe, offer his Sandhya prayers and
the day’s worship of Vishnu, and then go to some river or other sheet
of water and perform the Sradha ( funeral obsequies) of all his
ancestors. He should methodically offer oblations ( Tarpan ) to the
eight gods connected with the funeral ceremony, chant the necessary
vedic hymns and perform the gift ( dana ) and other duties of the
occasion.
These funeral rites may extend over seven or eight days, after which
he must have his beard, moustaches and head shaved off, keeping only
the scalp lock (Shikha ).
Next he must give away all his earthly possesions except a
lion-cloth (Kopin), a staff (danda) and a waterpot (Kamandal) with
ceremonies and Mantras appropriate to such an occasion. The sacrifice
(Yajna) performed at this time is called the Praja-pati-ahuti. Then
he performs the Viraja-homa by chanting the sixteen verses of the
Purush Sukta (Rigved, X. 90 ), and pouring out libation of ghee at
the end of every verse.
After performing these Yajnas, he renounces his children and friends,
saying ‘Listen, all ye : By the grace of my teacher I am eager to go
beyond worldly life. I have given up my attachment to
all. I have renounced my love for son, wealth and followers. You too
should give up your attachment to me, and not obstruct my
embracing of Sannyas.
Standing thus in the tank or river, he should take some water out of
it in the palm of his hand, and recite the Mantra, "Ö Earth,
I have become a Sannyasi. Om : Heaven I have become a Sannyasi. Om :
Hell, I have become a Sannyasi. “This is to be repeated thrice, with
voice modulated to three pitches. After throwing into the water a
full oblation of water taken into both his hands joined together,
while facing the east and saving, “May all creatures be free from
fear from me”
The next ceremony is that of discarding his sacred thread, and
cutting off the tuft of hair on the crown of his head (Shikha).
The last stage of the initiation:
After the new Sannyasi has come out of the water, cast of his clothes
and taken five or seven steps with uplifted face, as naked as at his
birth, his preceptor (Acharya), after prostrating himself before
him, would induce him to wear a loin-cloth (Kaupina) for decency
before ordinary men, and give him a staff (danda) to guard against
horned cattle, snakes &c. and a waterpot (Kamandalu ).
From Jivanmuktiviveka (p.15)
‘O Lord! How can I renounce all the actions ? ’ The disciple Aruni
asks his teacher Prajapati about the renunciation of all actions,
i.e., the seeker’s renunciation marked by the giving up of the tuft of
hair on the head, the sacred thread, the study of the Vedas, the
muttering of the Gayatri hymn etc. The teacher Prajapati gives him
instructions on renouncing all actions by saying ‘the tuft of hair’
etc. and enjoins to accept a staff, mantle, and loincloth, by saying
‘You should accept the staff etc’. And then he goes on to prescribe,
‘You should take bath at the three sandhyas, during meditation
concentrate on the Self, study the Aranyaka part of the Vedas, and the
Upanisads’. Thus the special duties of the sannyasa period of life—
which lead to knowledge—are prescribed for practice.
On being asked, ‘what is the course for the yogis, who are
paramahamsas ?’ by Narada, the teacher, Lord Prajapati advises as
before, the total renunciation of everything saying: ‘own sons,
friends, etc.’ and then says: ‘the loin- cloth, the mantle and the
staff should be accepted for one’s i own use and for the benefit of
the people at large.’ Thus indicating that the acceptance of the staff
etc. is only customary and by saying: ‘they are not the main thing’
(not the essential condition of Self-realization)…
‘Then what is the chief condition ?’ ‘This is the chief— neither the
staff, nor the topknot, nor the sacred-thread, nor the cloak, without
all these moves the paramahamsa. Thus the absence of the staff etc.,
the symbols of this sannyasa, is the textual commandment; saying this:
‘neither cold nor heat (affects the paramahamsa; and with these
words: ‘wearing the sky’s regions as his garment (i.e. naked) and for
him no convention of salutation etc.’, it is thus shown that the
paramahamsa is absolutely free from all social norms and conventions.
Just because the sampradhyas differ, this does not mean one is vedic and the other in anti vedic. All sampradhayas believe in Vedas and it is only intepretations. The six darshanas of sanatana dharma differ in so many ways: eternal hell, concept of mukti, jivanmuka, importance of bhakti/jnana, role of karma, author of vedas etc. but none of these darshanas are called anti-vedic. Other than the philosophical differences, even the conduct of samskaras such as upanayana, vivaha (marriage) and shraddha are very different in different sampradayas.
Vedas and smritis have different interpretations by different sampradayas. That does not mean the other is anti Vedic. I have clearly pointed out the various smriti and Shruti followed by dasanami sampradaya and I have also shown the texts followed by srivaishnavites. One follows the sampradaya one is born in usually. Unlike abrahamic religions, each sampradaya can follow its own rules and regulations based on their interpretations of the Vedas. Does not mean the other is anti Vedic.