First and foremost, Hinduism permeates much of India. You ll see the image of some deity or the other even in roadside eateries. On the bumper stickers. In our national song and national anthem. In much of the symbolism of Indian independence movement. It is not necessarily sinister. But it is ever present. Some of the symbolism is cultural, it just happens to derive its root from an India that was Vedic/puranik hindu. India has the gargantuan task to create a secular nation out of a society that’s majority hindu and historically hindu. And it’s an ongoing process.

Let’s take a short dip into the Origin of the word hindu or Hindi, it is an Arabic word for people living beyond Indus. It is equivalent to the demonym Indian. Thus, Hindu has for much of the history of the geographic region has meant Indian people. This is an argument that is used by some people and I will try to address it later on.

The official name of India - Bhārat Gaṇarājya - ( republic of India ) - comes from the legendary clan of Bharata from rig Veda that won the war of ten kings, or one of the two kings of that name. Northwestern India was called Bhārata-varṣa in the past. This could be deemed to be hindu iconography. But there were few other candidates ( one can see why Aryavarta could have been deemed unfit only a few years after the Second World War and prevailing racial theory of arya dravida of the time - which I will refrain from remarking upon.)

Indian National anthem anthropomorphizes mountains, rivers and oceans and shows them to be seeking holy blessings from The Vidhata ( closest is the Norse norns or Latin genius - vidhata writes the future of a child born ) of the destiny of India. This is a very hindu thing to do, if one were to look at it that way. The words, being in bengali, are closer to Sanskrit than hindostani would have been.

Indian National song “Vande Mataram” - anthropomorphizes India herself. Imagines the goddess of India - like Athena for Athens - an idea that’s much older than the songs. Again a decidedly hindu imagery.

I mention these because these are - more or less - undisputedly accepted. They are included in the constitution of India that “shall be a democratic republic” - secular added later.

Now we come to some of the more interesting examples : the North Indian classical music, called Hindustani music even in Pakistan, comes with a decidedly hindu mythology. And has a hindu pedigree. But again this is not sinister.

Up to this point, I hope I have established that anyone that’s an Indian - even if they be from a different religion or have no religion - is still implicitly or explicitly accepting hindu iconography because it’s part of our constitution. I, as an atheist, am included in it. It should show to you, OP, the complex way in which religions interact in a secular India. Anything hindu is not deemed antithetical to the idea of India BY DEFAULT, because Hinduism is so closely interwoven with the majority of the history of India. In fact, we’d have to discard much of Indian history and culture to arrive at a truly non-hindu Indian state.

What is sinister is the spread of ideology that would exclude others from being a full citizen of a secular India because of their creed, or geographic origins. And perhaps that is what you are asking about. And that finds roots in the Sangha movement. That can be traced back to RSS. Of course, until the idea of Pakistan comes to be, the idea of a hindu India does not have legs. Because the Muslims would have been prominent stakeholders of an independent undivided India.

As mentioned earlier, hindu is used by them to mean ethnic Indian regardless of religion, but this is not constitutional. As Indian constitution allows for naturalization of a foreign national. We do have quite a few Anglo-Indians, Portuguese Indians, French Indians who don’t fit this mould. Also, India has a community of parsis ( Persians ) and siddis ( Africans ) who have lived in India for centuries.

To conclude, Hinduism pervades all Indian nationalism. But some of it is antithetical to the idea of India, as defined in the constitution. This particular brand is less than a century old. Their ultimate dream is unconstitutional. That is not to say that the supermajority cannot change the constitution. But as it stands, anyone elected to office is still required to uphold the ideal of secular socialistic democratic republic that the drafters of the constitution envisioned India to be.