There is nothing called Modern Hindu.
"Modern Hindu" is simply a term of convenience that I use to describe the pseudo-Dharmics that inhabit the modern Republic of India. Many of these psuedo-Dharmics, especially of the self-proclaimed "right-wing" variety, also engage in hilarious but nonetheless harmful intellectual masturbation about a "glorious Dharmic past" which has never existed, and they themselves have no understanding of what Indic civilization or "dharma" represented. You are right that there is no such thing as a "Modern Hindu" per se, because classical Indic civilization and the concept of "dharma" are dead. What we have now are people who nominally refer to themselves as "Hindu", but whose actual worldviews and beliefs are distinctly shaped by outside forces, especially those of the Islamic and Western civilizations. The views and beliefs of these "modern Hindus" would be largely alien and incomprehensible to an actual member of Dharmic civilization from, say, the 7th century C.E. Which is NOT to say that the the Dharmic individual from the 7th century was "superior" in any way to the pseudo-Dharmic "modern Hindu" of the 21st century, just that they are as fundamentally different from each other as Ahmadinejad is from Cyrus the Great, despite both of them being "Persians".
We don't follow a yuppie version of a Desert Ideological Cult.
Actually, yes, you do. At least, the "Hindutvadis" and like-minded "modern Hindus" do. Their philosophy and ideology is directly influenced and shaped by Islam, and indirectly by Christianity by way of Western colonialism.
An interesting example of pseudo-Dharmic modern "Hinduism" that I recently stumbled upon was a statement by Shastra Dharma Prachar Sabha (henceforth abbreviated SDPS) in the years shortly following India's Independence, regarding the Hindu Code Bills. SDPS was vociferously opposed to several aspects of the proposed reforms to Hindu marriage law, including the introduction of divorce, provision for intercaste marriage, and moves against bigamy (so much for "Hindu liberalism"). These views are startling in themselves for their backwardness and disregard for basic human dignity, especially those of women. But what was really interesting to me, was the justification that SDPS gave for their views. They said, and I quote,
"The [Hindu Code] bills go against fundamental principles of the Hindu Shastras, God's spoken words, on which the society is based." (end quote).
Link:
Religious Conscience, the State, and the Law: Historical Contexts and ... - Google Books
The reference to "God's spoken words" is a clearly Abrahamic and, in particular, Quranic, view of a religious-legal tradition. SDPS was legitimizing their views in much the same way that a Sunni Muslim qadi would. Such a view is alien to Dharmic tradition, since "dharma" as a religious-legal tradition was never historically legitimized in the same way that the Muslims (for example) legitimized the Sharia, i.e. by appealing directly to "God" and claiming that the Sharia was the infallible word of God himself. Ancient Dharmics did not have such a view of their religious-legal tradition, because they did not share the Abrahamic concept of "God" in the first place, and the idea of a body of law being infallible because it is "God's Spoken Word" would have made little sense to ancient Indians. The views of SDPS, the self-proclaimed "authority" on "dharma" and Dharmic religious-legal tradition, was using Abrahamic terms to describe and justify their views! This is hardly unique to the SDPS, and can be observed across pseudo-Dharmic modern "Hindus", who are unable to understand the civilization that they profess to belong to, because their 'roots' lie more in the Islamic and Western civilizations than they are willing or able to recognize.
@LurkerBaba should provide his views here.