How does AP justify caste affirming verses and karma based rebirth in Brahma Sutras and Upanishads

Brahma Sutras have the famous “Apashudradikarana” section baring Shudras from taking up Vedanta study.

And Chandogya Upanishad in 5.10.7 says

“Those whose conduct here has been good will quickly attain a good birth — the birth of a Brahmana, the birth of a Kshatriya, or the birth of a Vaishya.
But those whose conduct here has been evil will quickly attain an evil birth — the birth of a dog, the birth of a pig, or the birth of a Chandala.”

तद्य इह रमणीयचरणा अभ्याशो ह यत्ते रमणीयां योनिमापद्येरन् ब्राह्मणयोनिं वा क्षत्रिययोनिं वा वैश्ययोनिं वा ।
अथ ये इह कपूयचरणा अभ्याशो ह यत्ते कपूयां योनिमापद्येरन् श्वयोनिं वा सूकरयोनिं वा चाण्डालयोनिं वा ॥

This particular verse challenges AP’s view of rebirth and caste together.