Is it an obligation to be a Brahmin to study advaita vedanta ?
1Well depends on what you mean by study exactly.– Ravi PatelMar 6, 2022 at 21:43
For the Brāhmaṇas he ordained teaching, studying, sacrificing and officiating at sacrifices, as also the giving and accepting of gifts. (Manu Smriti 1.88).
Teaching and studying, offering sacrifices and officiating at sacrifices, and giving and accepting gifts are the six occupations of a highest-born person. - Manu Smriti 10.75
Now, the question is what we mean by studying. Commentator of Manusmriti - Medhatithi did not throw any light on it. However, this has been made explicit in other Smritis.
The duties of the Brāhmaṇa are six: studying the Veda, teaching, sacrificing, officiating as a priest for others, giving alms and accepting gifts. - Vaśiṣṭha 2.13-14
Every twice-born one is entitled to prosecute the study of the Vedas, to celebrate Vedic sacrifices and to practice charities. Of these, teaching, the celebration of religious sacrifices (for others), and acceptance of gifts are functions which specifically from the right of a Brahmana. - Gautama 10.1-3
Thus, you see that studying Vedas is an obligation, but studying specifically Advaita Vedanta is not an obligation. Just to clarify, Advaita Vedanta interprets Vedic texts in a specific way. But there are other interpretations as well (For example, Dvaita Vedanta etc.) Which interpretation you would read depends on your likings.