this is not a duplicate of
in answer to which the words of Arjuna are cited:
1.41 - When unrighteousness prevails, O Krishna the women of the clan become corrupt; when women become corrupt, there arises intermixture of castes.
adharmābhi-bhavāt kṛṣṇa praduṣyanti kula-striyaḥ | strīṣu duṣṭāsu vārṣṇeya jāyate varṇa-saṅkaraḥ || 41 ||
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.
doṣair etaiḥ kula-ghnānāṁ varṇa-saṅkara-kārakaiḥ | utsādyante jāti-dharmāḥ kula-dharmāśca śāśvatāḥ || 43 ||
This question asks did Krishna, in his own words, support birth-based caste.
Because of the infinite ambiguity of Sanskrit, Swami Mukundananda, denies that even Arjuna was talking about caste:
दोषैरेतै: कुलघ्नानां वर्णसङ्करकारकै: | उत्साद्यन्ते जातिधर्मा: कुलधर्माश्च शाश्वता: || 43||
BG 1.43: Through the evil deeds of those who destroy the family tradition and thus give rise to unwanted progeny, a variety of social and family welfare activities are ruined.
This question asks what Krishna said, in his own words about birth-based caste.