What Advaita tells about
Mleccha can change religion to Hinduism?
(Yes means which varna they will come. No means explanation of why they should not change religion)
Then any justify to a Chandala
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Excellent question. The two are separate matters. Advaitha Vedanta is a philosophy of mind and spirit, based on Upanishads, Bhagavad Gita and Brahma-sutras. It discusses the three realities; Brahman, Jiva and Jagat and prescribes a methodology for achieving the highest goal - moksha. The Varnashrama Dharma is an economic theory not a philosophy. It is a complex system for social management in the age of a balanced economy. The system in its pure form aims at the optimization of the three goals of human life - the tripod of material happiness; Dharma - occupation and value system for the society and individual, artha - production and expenditure of wealth, and kama - enjoyment, recreation, procreation etc. These two aspects of life are known as trivarga - the three material goals of the householder and apavarga - ultimate liberation from samsara - the goal of the renunciates. So one can indeed study and practice Vedanta without any reference whatsoever to the caste system. One can also practice the caste system without any reference to Vedanta - which is generally the case. The message of the Gita is an integrated system and all three goals of human happiness should be striven for, but without attachment but rather in a spirit of renunciation.
I want to be brief and just remind you that the caste-system is an extremely complex network of kinship and social relations involving transactions of goods and services. It has been very flexible over the generations but in its present form is a complete corruption and travesty - since society has dramatically changed since its formulation. The problems of the caste system are the same as any economic system - corruption, greed, oppression, exploitation etc.. There is no economic system in the world that is pure and benevolent - neither capitalist or communist.