Is it really true that 'Brahminical Patriarchy is a fair & entirely mainstream phrase'? What about 'Jewish Capitalism'? Surely that is not a mainstream phrase? It unfairly stigmatises a particular set of people on the basis of their ancestral religion. Moreover, it imputes occult powers and sinister motives to a group of people no different from their neighbors of other faiths or communities.
I suppose it could be argued that Rahul Gandhi's claim to the Premiership of India is an example of 'Brahminical Patriarchy' because he now declares himself a Brahman and his father and great-grand father held that position before him. But there is no need to 'smash' this example of Brahminical Patriarchy because people are free to vote for whom they please.
Barkha Dutt says that 'Brahminical Patriarchy' is a mainstream phrase ' in the way that we now know the intersectionality of Feminism & the critique of upper caste hegemony'. Does she really believe that 'intersectionality of Feminism' is a mainstream phrase? Does the average American use this term? I see from Wikipeidia that the first person to use it was one Kimberle Williams Crenshaw- a Professor at Columbia (where Barkha studied) in 1989. Since then it has gained no traction among ordinary people. Rather it features in an elite academic availability cascade more famous as a target of satire than for any real world achievement or accomplishment.
Similarly the Gramscian term 'hegemony' is associated with the elitist 'Subaltern School' scarcely any of whom remain domiciled in India. No one could understand what these people were talking about and they have had no political influence whatsoever.
Caste is a reality in India. To speak of 'Brahman patriarchy' is to attack a particular group of people who will respond in like terms. Barkha Dutt says 'it is NOT an attack on Brahmins but on hierarchy much like White Privilege'. However, in India, it means don't vote for X because he is a Brahman. Since most Brahmans are poor where they are numerous, it is not the case that any 'hierarchy' is being attacked. Rather, it is a particular group of people who will retaliate in like terms if they are able to do so.
Talk of 'White Privilege' may seem innocuous- more especially to dark skinned people like myself. However, it has created a backlash and polarised Society in the US. White people in certain occupational/regional groups can see their life-chances have declined relative to other groups. If White Privilege was what enabled them to prosper previously, then they will fight to impose it once again. There is no point in stigmatising people according to their birth or colour. They will retaliate in like terms. When it comes to 'smashing' things, they may turn out to be more effective. Why provoke them to do so if your aim is to improve Society by lifting up weaker sections?