The sanskrit word for sect is 'sampradAya'.
According to sanskritdictionary.com, 'sampradaya' means
bestower (Monier-Williams, Sir M. (1988))
any peculiar or sectarian system of religious teaching (Monier-Williams, Sir M. (1988))
established doctrine transmitted from one teacher to another (Monier-Williams, Sir M. (1988))
presenter (Monier-Williams, Sir M. (1988)
So 'sampradAya' is a concept as old as that of 'Guru'.
The 'ParasurAma-kalpasutra' (https://www.scribd.com/doc/130237345/Parasurama-Kalpa-Sutra-in-English-First-30-Verses) (1/2) writes
sampradAyah guruparamparA-achara-anusaranam, meaning: SampradAya means the following of the religious rituals in accordance with the lineage of the gurus.
sampradAya-vishvAshAvyam sarva-siddhih (Ibid, 1/9) meaning that following the sampradaya and having faith is the root of success.
There are some branches of the Vedas, like the 'KAnva' branch which could be seen as the origin of the lineage system or sampradAya.
Another source is the Mantra-yoga-Samhita, which states
AkAshasya-adhipo vishnur agnes cha api maheshvari/vayor agnir kshiter isho jivanasya ganAdhipah.Meaning : The Lord of the Akasha-Tattva is Vishnu [and so the individuals in whom AkAsha-tattva is dominant would worship Vishnu ie be 'Vaishnava' etc], of Agni-tattva is Mahesvari, of Vayu-tattva is Agni or Surya, of kshiti-tattva is Shiva and of jala-tattva is Ganesha.
An able Guru gives mantra judging the dominance of the tattvas in the spiritual body of the disciple and according one can be Vaishnava or Shakta or Saura or Shaiva or Ganapatya.
So 'Sampradaya' can be named after the Gurus, like Sankara sampradaya, Ramanuja sampradaya (or the Vedic KAnva branch) or can be named after the chosen deity, like Vaishnava sampradaya or Shaiva sampradaya. Both are accepted in the Sanatana Tradition.
Here, the concept :'ekam sad viprA vahudha vadanti' of the Vedas is very clear.The same God is named differently according to the inclinations of the devotees and there is NO scope of degrading any form of God, as you mentioned in your comment. To make the devotees mind one-pointed, different scriptures have sung glories of the different forms and the 'Supremacy' is actually dependent on THE DEVOTEE'S SANSKARA and NOT ON THE REAL SUPREMACY OF ANY FORM. This is known as 'na hi nindA-nyAya'. This is the real source of 'Sect'.
Swami Vivekananda says regarding the origin of sect and secterianism :
There have been sects enough in this country . .and there will be enough in the future, because this has been the peculiarity of our religion that in abstract principles so much latitude has been given that, although afterwards so much detail has been worked out, all these details are the working out of principles, broad as the skies above our heads, eternal as nature herself. Sects, therefore, as a matter of course, must exist here, but what need not exist is sectarian quarrel. Sects must be but sectarianism need not. The world would not be the better for sectarianism, but the world cannot move on without having sects. One set of men cannot do everything. The almost infinite mass of energy in the world cannot tie managed by a small number of people.
Here, at once we see the necessity that forced this division of labour upon us — the division into sects. For the use of spiritual forces let there be sects; but is there any need that we should quarrel when our most ancient books declare that this differentiation is only apparent, that in spite of all these differences there is a thread of harmony, that beautified unity, running through them all? Our most ancient books have declared: — "That which exists is One; sages call Him by various names." Therefore, if there are these sectarian struggles, if there are these fights among the different sects, if there is jealousy and hatred between the different sects in India, the land where all sects have always been honoured, it is a shame on us who dare to call ourselves the descendants of those fathers.
Lack of understanding of this truth leads to another starting of 'sect' that leads immediately to 'secterianism'. Sri Krishna Prem,(https://en.m.wikipedia.org/wiki/Krishna_Prem), the famous siddha Gaudiya-Vaishnava writes in this context in His 'The Search for Truth'(1938):
Every belief has the its corresponding doubt lurking somewhere in the shadow.It is for this reason that men of strong religious beliefs become so fanatical. Silently gnawing at their hearts, insidiously whispering in their ears, is an army of doubts..that whispers to lay those ghosts (of doubts) in the basement, that the believer strives with all his might to convert others into his creed...filled with an inner hatred of himself, he vents his explosive anger on others.Thus from a mere fanatic he becomes a persecutor (pages 3-4).
In the above lines, Sri Krishna Prem has explained the meaning of 'sect' which leads to secterianism and hatred and demeaning of Forms worshipped by others. So, while writing on the 'Worship of God', is writes in the same book (page 20)
In the first place, we may set aside the disputes as to whether to worship God as Shiva or as Vishnu, as Rama or as Krishna, because the Shruti has declared and the Mahapurushas have confirmed that all these Forms are forms of the one Supreme 'ekam eva advitiyam'.The choice for any one of them as one's Ishta is one that depends on 'samskaara'. All worship should be directed towards the one Supreme Reality, and ,whichever Form be selected, it should be conceived as an embodiment of the Supreme and Changeless One.
Forgetting the above gives rise to 'sect(arianism) and so ignorance is one origin of 'sect'. Swami Vivekananda therefore warned us :
Sectarianism, bigotry, and its horrible descendant, fanaticism, have long possessed this beautiful earth. They have filled the earth with violence, drenched it often and often with human blood, destroyed civilisation and sent whole nations to despair. Had it not been for these horrible demons, human society would be far more advanced than it is now.
He repeatedly reminds us about the dangers of 'Secterianism' and provides a beautiful solution to smash it also :
There is no salvation for man until he sees God, realises his own soul. Therefore, above all, let us understand this, and the more we understand it the less we shall have of sectarianism in India, for it is only that man who has realised God and seen Him, who is religious. In him the knots have been cut asunder, in him alone the doubts have subsided; he alone has become free from the fruits of action who has seen Him who is nearest of the near and farthest of the far. Ay, we often mistake mere prattle for religious truth, mere intellectual perorations for great spiritual realisation, and then comes sectarianism, then comes fight. If we once understand that this realisation is the only religion, we shall look into our own hearts and find how far we are towards realising the truths of religion. Then we shall understand that we ourselves are groping in darkness, and are leading others to grope in the same darkness, then we shall cease from sectarianism, quarrel, arid fight. Ask a man who wants to start a sectarian fight, "Have you seen God? Have you seen the Atman? If you have not, what right have you to preach His name — you walking in darkness trying to lead me into the same darkness — the blind leading the blind, and both falling into the ditch?"
Reference : Satramulak Bharatiya Shaktisadhana,Upendrakumar Das, RMIC, vol. 1.
In the Brahma-Sutras, we find mention of the Pasupata and Pancharatra sects and both have been called Non-Vedic.Thefore in real sense, the sect in the Vedic Culture seem to have started with Gaudapada of the Advaita School.He was the first human Acharya of the Advaita sect.
The division of the Vedas among various sages for the proper preservation of the Veda-mantras and as a result the emergence of the various sakhas (like the Kanva Sakha I mentioned) can be theoretically taken as the origin of the concept of Sect, because that is also starting of some lineage.
Except these two, I think we have no evidence in the Vedic or Vaidantic literature about the origin of the sects.