Reddit reviews Unifying Hinduism: Philosophy and Identity in Indian Intellectual History (South Asia Across the Disciplines)

This is essentially correct but its a complex process. Indians (Hindus) have always had a rich tapestry of pagan mythology, folk religion, and animist beliefs. The word Hindu was an ethnoreligious designation during Muslim rule and transitioned to a purely religious designation during British rule. But the origins of that transition began during Muslim rule. Now here's a quirk to really confuse you, the Gurus talks about Hindus and their Vedas as though its a single religion and equivalent to Islam and the Quran. My personal opinion is that they generalized the tapestry of Hindu beliefs into a single group in their bani for simplicity sake but would've dismissed the idea of a single coherent religion called "Hinduism".

Just remember that as Sikhs its not our mission to dismantle other people's religions, and at this point most Hindus think there is a real religion called Hinduism which they are a part of. In terms of what is real and what's not, "Hinduism" is more real than the Mormon religion. But if some Hindu extremist guy starts saying Sikhi is part of "Hinduism" you are then at liberty to state your views. Here's a couple books that go into this topic in detail:

Was Hinduism Invented?

Unifying Hinduism