This is a much needed discussion. It is very relevant to modern Indian and Hindu politics. Therefore, I felt the need to explain a bit of its recent history.
Hindutva is a victim of its nomenclature. When the term was first coined, using "Hindu" as a geographical reference was common, and even the British referred to Indians as "Hindoos" So political nationalist philosophers in India at the time who were fighting against British rule, had to come up with an alternative identity for India from the one the British imposed on them --- which basically was no identity at all: India was defined in terms of invaders and history of India was nothing but just non stop invasions and warring states. There was no "India" to speak of, and no "Indian culture" and anything that thought to be "Indian" was brought in by invaders. The British brought democracy, rule of law, railways and industy; the Muslims brought architecture, cuisine and devotion to one God(then inherited by Sikhism) and the Greeks brought art, philosophy, mathematics and logic. The Aryans brought Sanskrit and Vedas. In other words, there was nothing "Indian" ever. India is just a "construct" this position is taken even seriously today, as the recent attempts by "Seculars" in US made an attempt to change "India" into "South Asia" in discourse
This colonial narrative of India, is the same narrative you hear the specularists and the communists of India still repeat today. The NCERT history books for example only look at those periods of history where there was an invasion. First it is the Aryan invasion, with the coming or now "migrating" Aryans bringing Vedic culture. Then it is the Greek invasion, with the Greeks setting up Indo-Greek states where later Indian philosopy flourished by borrowing the concepts from the Greeks. Although today, some scholars begrudgingly accept some Indian philosophical ideas were original because they are older, to a large extent they consider the so-called golden age of India the Gupta age where literature, astronomy, mathematics and the the economy flourished, as a result of earlier Greek influences. Then it is the Mughal invasions and finally the British invasions.
Many periods of Indian history are missing. The the pre-Greek periods i.e. pre Mauryan are scarcely mentioned, but this is the ACTUAL golden age of India, when great Hindu scientists, philosophers and dramatists flourished such as Susrutha, Charaka, Patanjali, Pingala, Kautaliya, Kapila, Kannada, Kapila, Bharata, Vyassa etc flourished. This is the period when the first universities and hospitals were built in India. This is the period when we find earliest Bhakti sects.
But the history books have been so muddled up, that a lot of pre-Mauryan developments get dated to the Gupta age. For example Susrutha is 600BCE by most records, he was a professor of surgery at Kasi university, but you will find dates of Susrutha as late as 500CE.
Gautama Aksapada, the founder of Nyaya is suppose to have been around the same time, but his dates have been moved to 200CE, because it is assumed Nyaya was influenced by Greek logic
The reason why many Indian people have not heard of this period and the great people of it, is well because they are "Hindu" It is convenient to start the narrative of urban India from the Mauryans because they are Jain and Buddhist. This is the "secularist" narrative of modern India and hence the emblem for the Republic of India is the "Ashoka chakra" of Asoka who is seen as a "secular" king. It is not just in the pre-Mauryan period that Hindu history gets ignored, but even post-Mauryan periods. Many chapters of Hindu history such as the Chola, Pandyas, Sri Vijaynagra, Vikramadiya, Harishchandra, Bhoja, Marthas, Sikhs get scarcely a footnote. This gives the impression there is no "Hindu" history. Indian history is mostly the history of non-Hindus. It is tantamount to erasing Hindu civilisation from history.
So in the earlier half of the 20th century, nationalist Hindu Indian philosophers had to resist against this attempt by the colonialists to erase them from history books, so they came up with "Hindutva" as an attempt define Indian history, heritage, culture and identity. The term "Hindu" was not divisive then, so at the time "Hindutva" was seen as empowering and characterised the spirit of the Indian independence struggle. It was synonymous with Indian nationalism and freedom for Indians.
However, post independence, the word "Hindutva's" connotations have changed, it is no longer a geograhphical reference, it refers to specific religious group called the Hindus in India in opposition to non-Hindus living in India, and hence it is perceived as fascist by non-Hindus. Muslims, Christians, Buddhists, Jains and even Sikhs unite against it as a tyranny of the majority Hindus. If the term was changed to say "Bharatva" or "Dharmatva" it may be less divisive. I think the BJP to an extent has realised this, so that is why in 2014 Manifesto they did not use the term "Hindutva" but instead "India chitti" that is recognising Indian has its unique and ancient consciousness.
The seculars have been successful in making "Hindutva" a bad word, conjuring up other other words like fascism, fundamentalism , Nazism, intolerance and terrorism when used. They have had almost 70 years to spread the propaganda and have controlled the culture industries of India like the print media, film and television and academia. These ideas are firmly entrenched in Indian socialist minds. Even though the Congress-rule is over India, the Congress mentality still controls the elites of Indian culture e.g. Recently, when the BJP tried to replace the head of FTII with a pro-Hindutva figure, a wave of socialist and communist filmmakers, writers and academics, considered highly established and acclaimed, lead a month long protest. They became known as the "award vapsi" gang, because they all returned their national awards they won in the past for their works. This also became known as "intolerance" Another replacement by BJP recently was the head of RBI(Reserve Bank of India) another secularist with a pro-Hindutva banker.
The new resurgent BJP which has previously fought elections on the Hindutva platform and and lost out to the secular propaganda, has realised this and under the aegis of Modi has changed its plaform to "development" which has struck a chord with all Indian and Hindutva has taken a back seat, now called "Soft Hindutva" which is just about tolerable to non-Hindus now. It may help the BJP cause to change the name now to something like Bharitya and define a Bharatiya culture, history, heritage and identity which all Indian people can accept. I can already see strong evidence of something like this shift happening, with the recent rise of Indian nationalism. As India becomes more developed, Indian people are becoming more confident in asserting themselves and their past glory. It is not uncommon to hear Indian people say things like "India was the richest nation on Earth before the British came" and now even top previous socialist elites like Shashi Tharoor are singing the tune.. He recently when viral for his speech at the Oxford Debating society for exposing how Britain impoverished India, coming to an India that had 24% or so of the industrial output in the world in 1700 to 2% when they left.
More and more Indians are now learning of great Indian Hindu scientists like Surutha, famous for plastic surgery or Kanada famous for his theory of atoms, largely because of the access to the internet has allowed these facts to circulate. The internet has become a powerful medium of education for a lot of new generation Indians. There was a time when India scientific schools like Nyaya-Vaiseshika, the early analytical and natural philosophers of India were just obscure names only experts in Indian philosophy knew, but now more and more lay people are learning about its existence, especially from other Indians on forums like this. Panini as the first computer scientist has became a popular meme and even ideas like renaming Bakus-Form to "Panini-Bakus-Form" have been suggested. Another suggestion is to rename "Pythagoras theoem" to Baudayana theorem, from where Pythagoras originally got if from. This trend is going to continue over the course of this century, as India emerges as the first or second most powerful country in the world.
What Indian people do need to stay clear off though because it undermines the credibility of the real claims, is to stay away from claims of ancient cloning, vimanas and nuclear weapons. There are lot of over enthusiastic Hindus who go around the internet making these claims, that the legitimate and verifiable claims like Susrutha get thrown away with the bathwater too.