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Such as
1.41 - When unrighteousness prevails, O Krishna the women of the clan become corrupt; when women become corrupt, there arises intermixture of castes.
1.43 - By the crimes of the clan-destroyers who bring about intermingling of castes, the ancient traditions of the clan and caste are destroyed.
Can Arjuna's statements in Bhagavad Gita be taken as pramAna i.e., are they on par with Krishna’s?
Yes. All ancient Vaidika commentators take that as a pramana and for good reasons that I will explain.
Arjuna was worthy enough to receive the teachings of the Gita personally. To not believe him is equivalent to rejecting the Gita itself.
He is also re-iterating to Krishna the beliefs that were common during his time and even before: that the caste system is birth-based. Arjuna's claim is made by other reputable people in the Mahabharata like Yudhishthira, Bhishma, etc.
Bhishma, the speaker of the auspicious Vishnu Sahasranama, says the same thing:
...by uniting themselves with women of other castes, led not by considerations of righteousness but by uncontrolled lust, cause numerous mixed castes to come into existence whose occupations and abodes depend on the circumstances connected with the irregular unions to which they owe their origin.
Moreover, this claim is made by the Vedas themselves, and Jaimini has even written a sutra for it in the Purva Mimamsa Sutras, which are also commented upon by Shabara:
The Vedic verse is:
"We do not know if we are Brahmanas or non-Brahmanas ... Therefore, When the pravaras [ancestral lineages] are being recounted, one should say the deities are our ancestors- (Maitrayaniya Samhita 1.4.11 of the Krishna Yajur Veda).
The Vedic verse shows that the castes are based on ancestry (gotra), and hence, birth-based. If caste wasn't based on ancestry, then it would be useless to mention pravaras in that verse in relation to caste.
The Mimamsa Sutra for that verse is:
On account of the failings of women, (there can be no certainty regarding one's caste); specially as the son belongs to the progenitor. - Adhyaya 1, Pada 2, Sutra 13
And Shabara's commentary:
It is difficult to know if one is really a Brahmana; - and this is what is figuratively spoken of as "we do not know", and the difficulty in knowing it for certain is due to "the failings of women", and also to the fact that "the son belongs to the progenitor"; this is also indicated by the advice "May you guard this dynastic line with great care." - Apastamba Dharma Sutra 2.6.13.6
Now to reject Arjuna's statements as apramana, is to reject authorities like Arjuna himself, the honorable recipient of the Gita, Shabara, Jaimini, the Pandavas, the Mahabharata, Bhishma, Vishnu Sahasranama, Krishna, and even the Vedas themselves.
This is to be expected from neo-Vedantins anyways, since they are after all, unorthodox.
The answer depends on what Arjuna himself thought of Krishna's teaching given in the Gita. Arjuna in fact asked Krishna to again lecture his Gita teachings after the end of the war. Krishna was annoyed with Arjuna and gave a summary of the Gita teachings which is known as Anu Gita.
Having been thus addressed, the greatly energetic Krishna, supreme among eloquent ones, embraced Phalguna and replied in these words, "I made you listen to something that is eternal and secret. O Partha! That was about the nature of eternal dharma for all the worlds. I am greatly displeased that you have ignorantly not grasped what I told you. O Pandava! It is evident that you have not been faithful, or your intelligence is not adequate. That dharma is sufficient to obtain the state of the brahman. However, I am incapable of telling you everything in detail again. I immersed myself in yoga and told you about the supreme brahman. But I will tell you about an ancient history with the same purport. Using that, if you use your intelligence, you will reach the ultimate destination, O best among those who uphold dharma! ...
Mahabharata, Ashvamedhika Parva, Chapter 1851 (16) translated by Bibek Debroy
This episode suggests that Arjuna himself recognised the worth of Krishna's teachings in the Gita and made no claim that his stray comments are of any importance. Hence Arjuna's statements are not pramana.
