If a Brahmin doesn’t perform duties as per his varna, is he still called as brahmin?
No. He will be considered degraded then. He will be a Brahmin just for the namesake.
From Manu Smriti:
2.103. But he who does not (worship) standing in the morning, nor sitting in the evening, shall be excluded, just like a Sudra, from all the duties and rights of an Aryan.
From VYasa Smriti , chapter 4:
A Brahmana, who has not studied the Vedas, is like a wooden elephant, or a leather-deer, but bear the name of the genus he belongs to. (37)
Like a deserted hamlet, like a waterless well, a Brahmana, who has not read the Vedas, is a Brahmana only in name. (38)
Grains of rice given to an unholy Brahmana, who has broken his vows and neglected the study of the Vedas, begin to cry in dismay, saying, " what evils have we committed to be punished with such a degradation.
And, from the Parashara Smriti:
Brahmans who know not the Gayatri relating to Savita, who are unacquainted with the Sandhya prayers, and with the sacrifice of fire, and who betake to tillage, — are Brahmans in name only
If Brahmans, the mere bearers of a Brahman's name, presume to prescribe a penance for sin, — they are guilty of a sin, and are destined to go to hell.
A Brahman, ignorant of the Gayatri hymn, is more unclean than even a Shoodra ; the Brahmans who know the nature and the sanctity of the Gayatri hymn, are honored and revered by all persons.
Also, in afterlife a Brahmin, who has not performed his duties well, becomes a particular preta as mentioned in the following verse:
Manu Smriti 12.71. A Brahmana who has fallen off from his duty (becomes) an Ulkamukha Preta, who feeds on what has been vomited; and a Kshatriya, a Kataputana (Preta), who eats impure substances and corpses.
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