Once a year since 1950, India tries to convince the world (and itself) that it is indeed a superpower, with an epic show that takes over the grandest road in India, the Rajpath in New Delhi. The Republic Day parade celebrates India's nationhood with pomp and circumstance. This year, however, there has been a flurry of calls to boycott the event. For the first time, the Indian middle class is disassociating itself from this hoopla. The barbaric Delhi gang rape in December may have been the trigger, but, beyond that, there is widespread disappointment with law and order and the political class.

The appeal for a boycott started on social media. It was soon labelled anti-national by traditionalists. Not surprising in a country riven down the middle, but the fault lines are not Hindu-Muslim, class or gender based; the breach is between two Hinduisms.

Hinduism is an odd religion. It works very well as a way of life but no longer works as a faith. It's too old, too corrupt, has moved too far from its raison d'être. For the educated urban Indian, Hinduism is a cultural rather than religious identity. They embrace all that's enjoyable about the Hindu way of life: the festivals, the food, the colourful mythology, sophisticated classical music and dance. They may go through the motions of worship on occasions but have no real faith in their pantheon of gods and goddesses, some of whom are decidedly strange. Nor do they follow the proscriptions that have crept into Hinduism over the centuries. Practised thus, Hinduism is the most laidback and accommodating of religions.

But there is the "other" Hinduism thriving in the small towns and villages of India, a harsh, religion that oppresses women and the "lower castes". The dark side of India's economic boom is that the largely uneducated adherents of this form of Hinduism are pouring into every corner of India. They are on a collision course with the laissez-faire middle-class Hindus of the cities. These often "upper caste" Hindu men of the hinterland pour into the cities in droves, where they find themselves disabused of their fondest beliefs, such as their superiority over women. That's when atrocities against women – such as the recent outrages that have shaken India – happen. And the resurgent Hindu fundamentalist parties and publicity-hungry self-styled holy men manipulate these zealots for their own ends.

Hinduism as a way of life works; it is inclusive and fun. It could knit the nation together but, in the face of the orthodox onslaught, it lacks bite. Enter the Brahmo movement. The Brahmos were 19th-century reforming crusaders, Hindus who sought inspiration from global liberal philosophies as well as the best traditions of Christianity and Islam to weed out the corruption that had crept into Hinduism. They were monotheistic and women were at the core of their crusade. Brahmo women were ordained as priests and became literary lights in Bengal. Together with their men, they agitated successfully for an end to the funeral practice of "sati" (the burning of the widow on her husband's funeral pyre. Like all reforming movements, there was a zeal about the movement that could, if resurrected in India now, combat the rise of the uglier face of Hinduism.

My family is a microcosm of this principle in practice. With an atheist Hindu (entirely possible in India) father and a Brahmo mother, our family prized girls: we were educated thoroughly and brought up to be equal (if not ever so slightly superior) to men. Four generations of women from our family excelled at university, learned to question everything, yet also embraced the energy and exuberance of myriad Hindu festivals.

But Brahmos, for all their progressive qualities, were puritanical and censorious about some of the things that define India: colour, gaiety and sensuality. Stamping out all that's joyful about India would not cure its ills, but a large dollop of Brahmo liberality into the larger cauldron of Hinduism would help make it a more equitable society.

This fusion of exuberance and tolerance has been practised for scores of years by the educated Indian middle class, but without real awareness of what's in the mix. The apathetic middle class has just begun stirring from a decades-long sleep, but if it could harness the energy of the independence-era reformers to stem the rot, could real change be far behind?