Even if earlier Varna was not birth based, and later it degenerated into birth base Varna and even later into birth based caste system. But whether there are counter arguments within Hinduism(esp. Hindu scriptures) regarding this degeneration into Birth based Varna/Caste system?
यस्य यल्लक्षणं प्रोक्तं पुंसो वर्णाभिव्यञ्जकम्।
यदन्यत्रापि दृश्येत तत्तेनैव विनिर्दिशेत् ॥३५॥
If one shows the symptoms of being a brāhmaṇa, kṣatriya, vaiśya or śūdra, as described above, even if he has appeared [born] in a different class, he should be accepted according to those symptoms of classification.
A Sudra is not a Sudra by birth alone--nor a Brahmana is Brahmana by birth alone. He, it is said by the wise, in whom are seen those virtues is a Brahmana. And people term him a Sudra in whom those qualities do not exist, even though he be a Brahmana by birth.
'In human society, O mighty and highly intelligent serpent, it is difficult to ascertain one's caste, because of promiscuous intercourse among the four orders. This is my opinion. Men belonging to all orders (promiscuously) beget offspring upon women of all the orders. And of men, speech, sexual intercourse, birth and death are common. And to this the Rishis have borne testimony by using as the beginning of a sacrifice such expressions as--of what caste so ever we may be, we celebrate the sacrifice. Therefore, those that are wise have asserted that character is the chief essential requisite.
A man, may be born in the Sudra caste, but if he is possessed of good qualities, he may attain the state of Vaisya and similarly that of a Kshatriya, and if he is steadfast in rectitude, he may even become a Brahmana.
From the kṣatriya known as Agniveśya came the celebrated brāhmaṇa dynasty known as Āgniveśyāyana.
Manu also had a son known as Dhṛṣṭa, from whom another sect of kṣatriyas was generated, but although they were born of one who had the qualities of a kṣatriya, they became brāhmaṇas."
In addition to these nineteen sons mentioned above, there were eighty-one younger ones, all born of Ṛṣabhadeva and Jayantī. According to the order of their father, they became well-cultured, well-behaved, very pure in their activities and expert in Vedic knowledge and the performance of Vedic rituals. Thus they all became perfectly qualified brāhmaṇas.
That wretched Brahmana who falls away from his duties and whose behaviour becomes wicked, becomes, O king, a Sudra.
Vishvamitra was a kshatriya king earlier. Later, he undertook intense penance and attained brahminhood. This is discussed here.
Bali Maharaj (son of a Daitya) will become next Indra. This is discussed here.
Shanti Parva of Mahabharata says people of all varnas can perform sacrifices as at first only Brahmin Varna was created, from Brahmin Varna only other Varnas emerged.
Bharadwaja said, 'If the distinction between the four orders (of human beings) be made by means only of color (attribute), then it seems that all the four orders have been mingled together. Lust, wrath, fear, cupidity, grief, anxiety, hunger, toil, possess and prevail over all men. How can men be distinguished by the possession of attributes? The bodies of all men emit sweat, urine, faeces, phlegm, bile, and blood. How then can men be distributed into classes? Of mobile objects the number is infinite; the species also of immobile objects are innumerable. How, then, can objects of such very great diversity be distributed into classes?'
"Bhrigu said, 'There is really no distinction between the different orders. The whole world at first consisted of Brahmanas. Created (equal) by Brahman, men have, in consequence of their acts, become distributed into different orders. They that became fond of indulging in desire and enjoying pleasures, possessed of the attributes of severity and wrath, endued with courage, and unmindful of the duties of piety and worship,--these Brahmanas possessing the attribute of Passion,--became Kshatriyas. Those Brahmanas again who, without attending to the duties laid down for them, became possessed of both the attributes of Goodness and Passion, and took to the professions of cattle-rearing and agriculture, became Vaisyas. Those Brahmanas again that became fond of untruth and injuring other creatures, possessed of cupidity,--engaged in all kinds of acts for a living, and fallen away from purity of behaviour, and thus wedded to the attribute of Darkness, became Sudras. Separated by these occupations, Brahmanas, falling away from their own order, became members of the other three orders. All the four orders, therefore, have always the right to the performance of all pious duties and of sacrifices.
Also, the very next chapter says Varna is not birth based.
Bharadwaja said, 'By what acts does one become a Brahmana? By what, a Kshatriya? O best of regenerate ones, by what acts again does one become a Vaisya or a Sudra? Tell me this, O foremost of speakers.'
"Bhrigu said, 'That person is called a Brahmana who has been sanctified by such rites as those called jata and others; who is pure in behaviour; who is engaged in studying the Vedas; who is devoted to the six well-known acts (of ablutions every morning and evening, silent recitation of mantras, pouring libations on the sacrificial fire, worshiping the deities, doing the duties of hospitality to guests, and offering food to the Viswedevas); who is properly observant of all pious acts; who never takes food without having offered it duly to gods and guests; who is filled with reverence for his preceptor; and who is always devoted to vows and truth. He is called a Brahmana in whom are truth, gifts, abstention from injury to others, compassion, shame, benevolence, and penance. He who is engaged in the profession of battle, who studies the Vedas, who makes gifts (to Brahmanas) and takes wealth (from those he protects) is called a Kshatriya. He who earns fame from keep of cattle, who is employed in agriculture and the means of acquiring wealth, who is pure in behaviour and attends to the study of the Vedas, is called a Vaisya. He who takes pleasure in eating every kind of food, who is engaged in doing every kind of work, who is impure in behaviour, who does not study the Vedas, and whose conduct is unclean, is said to be a Sudra. If these characteristics be observable in a Sudra, and if they be not found in a Brahmana, then such a Sudra is no Sudra, and, such a Brahmana is no Brahmana.
The question is specifically asking for counter arguments within scriptures that preaches against following a birth based system.
The strongest proof is provided in Manusmriti
3.109 A Brāhmaṇa should not advertise his family and Gotra for the purpose of obtaining a meal. Bragging about these, for the purpose of obtaining a meal, he comes to be called a “feeder on filth” by the wise.—(109)
Essentially, Brahmana cannot command any benefit, as much as even a meal, on the basis of his birth and if he does so it is equivalent of feeding on his vomit.
As per Manusmriti, respect is accorded to people in the below manner and as seen it has nothing to do with birth.
2.136 Wealth, Relation, Age, Action and Learning, as the fifth,—these are the grounds of respect; (among them) that which follows is weightier (than that which goes before it).—(136)
Brahmans commanded the highest respect because they were learned. It had nothing to do with birth. Thus it would be incorrect to say that default is birth based.
As mentioned in my answer here, Education is true birth
2.147: The birth that happens from womb of mother after parents desire for procreation is an ordinary birth. Real birth happens when the person completes his education
2.157: A Brahmin devoid of education is equivalent to an elephant made of wood or a deer made of leather. They are merely namesake and not real.
10.4: Brahmin, Kashtriya and Vaishya take second birth after education. Shudra who could not complete education is fourth Varna. There is no fifth Varna among Arya or noble people.
And just because a person is unable to complete education, it does not mean he is to avoided Varna migration can take place
P.S. Varna is derived from root word vṛṇóti which means choose for oneself.
There are countless examples in the sacred Itihasas and Puranas. But there are also a number of examples in Vedas themselves. Purusha Sukta itself is talking about the creation of 4 Varnas obviously not humans because we came with Manu and the Saptrishis. Rig Veda 9.63 says:
इन्द्रं वर्धन्तो अप्तुर: कृण्वन्तो विश्वमार्यम् । अपघ्नन्तो अराव्णः ॥
This is a prayer to make all humans Aryas. So when Krishna Yajurveda is making a distinction between Shudra & Arya it means bad people and noble people. Of course, birth is as per karma but this is a very clear message from the Veda itself that Varna can be changed! Now if we see Upanishads or Brahmanas we almost always get the same picture. Look at Chandogya Upanishad talks about the initiation story of another Upanishad's author:
Gautama asked him, ‘O Somya, what is your lineage?’ Satyakāma said: ‘Sir, I do not know what my lineage is. When I asked my mother, she said to me: “I was very busy serving many people when I was young, and I had you. As this was the situation, I know nothing about your lineage. My name is Jabālā, and your name is Satyakāma.” So, sir, I am Satyakāma Jābāla’. Gautama said to him: ‘No non-brāhmin could speak like this.
So the son of a highly impure shudra woman and unknown man was declared Brahmin. Now look at the story of Vedic author Vatsa found in Tandya Brahmana 14.6.6, Jaiminiya Brahmana 3.234:
The two sons of Kanva, Medhatithi and Trioka, contended about the sacred lore (brahman). They said : ' Come, let us cross the flaming fire'. They crossed the flaming fire. Tris'oka crossed over it (unharmed), but of the other it scorched the eye-lashes. Ho (Trisoka) said to him (to Medhatithi) : ' I have vanquished thee '. ' No ', said he, 'thou art the son of an Asura-mother ; even the deities have not wished to touch thee'. Then, they (said): 'Come, let us cross the water'. They crossed the flowing Rathaspa. Tris'oka crossed over it (unharmed), but of the other the rims of his cart were moistened by the water of the Rathaspa (translation uncertain, text corrupted !). He (TriSoka) said to him (to Medhatithi): 'I have vanquished thee'.
let us walk according to the rite through fire (to decide) which of us two is the better brahmin
Agni preferred Shudra's son. Shudra's son was a superior Brahmin compared to birth-Brahmin. Another example from the Brahmanas is in Kausitaki Brāhmana 12.3 and Aitareya Brāhmana 8.19
"You are the son of a female slave. We will not eat with you" (dāsya vai tvam putro si na vayam tvaya saha bhaksayisyama iti). Kavasa became angry and ran away. He recited a hymn of praise to Sarasvati, who then followed after him: sarasvatim etena suktena tustava tam heyam iyaya. Realizing what had happened, the surprised seers hurried to him to express their reverence: "0 seer, homage be to you. Do not harm us. You indeed are the best of us...
Saraswati considers a Shudra's son superior to all birth-Brahmins combined at being a Brahmin. The birth-Brahmins also accept they are inferior to him. He authored a part of Rig Veda. There are 108 canonical Upanishads as per Muktika Upanishad. One of them is Vajrasuchika Upanishad which says
It is said that a Brahmana is so because of his caste. This is not acceptable because there are diverse communities in the world... ...Among these many have attained the highest rank, despite of their lower birth and given proof of their wisdom. Therefore a Brahmana is not so because of his community.
Self-explanatory. I have given examples from 7 Vedic texts against caste.