From Sreemad Bhaagavatham
Srimad Bhaagavatham 7.11.35 (Canto 7: The Science of God, Chapter 11: The Perfect Society: Four Social Classes):
यस्य यल्लक्षणं प्रोक्तं पुंसो वर्णाभिव्यञ्जकम् ।
यदन्यत्रापि दृश्येत तत्तेनैव विनिर्दिशेत् ॥ ३५ ॥yasya yal lakṣaṇaṁ proktaṁ puṁso varṇābhivyañjakam
yad anyatrāpi dṛśyeta tat tenaiva vinirdiśetIf one shows the symptoms of being a brāhmaṇa, kṣatriya, vaiśya or śūdra, as described above, even if he has appeared in a different class, he should be accepted according to those symptoms of classification.
Now some argue that Bhagavad Geetha says that Guna is accumulated over years and set at birth. But they fail to see the core idea in it which says Guna can be both changed and transcended.
The story of adopted child Matanga to whom Indra said he could not change his Varna was mentioned in Mahabharatha. But is it authoritative? No.
From Shruthi
Rig Veda 9.63:
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!)
The case of Satyakaama Jaabala, which I cited elsewhere.
Vajrasuchika Upanishad:
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.
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.)
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
(And then Agni preferred Shudra’s son. Shudra’s son was a superior Brahmin compared to birth-Brahmin.)
From Smrithi
Mahabharata, Parva 3 (Vana Parva), Section 87:
At Kamyaka, Kusika’s son had quaffed the Soma juice with Indra. Then abandoning the Kshatriya order, he began to say, “I am a Brahmana”.
“ebhistu karmabhir devi subhair acaritais tathal sudro brahmanatam yati vaisyah ksatriyatām vrajet|!” (Mahabharat , Anusasana Parvan, 146.26) “Oh Devi, by performing these actions in this way, a sudra attains brähmana-hood and a vaisya attains ksatriya-hood.”
“sudre caitad bhavel laksyam dvije tac ca na vidyatel na vai sudro bhavecDchudro brahmano brahmano na call” (Mahabharat,Santiparvan, 189/8) “If this (list of virtues) is seen in sudra and it is not there in a twice born one, then the sudra will not be a sudra and the brahmana will not be a brãhmana.”