I don't have a source, but I'm a Hindu man who was initiated into the priesthood as a child and had to study it for many years. I'm not religious, but that was my upbringing.

Anyways, I think that Hindu orthodoxy had, for about 2000+ years, had a distinction between 'astika' (believers) and 'nastika' (nonbelievers). The difference between the believers and nonbelievers was based on whether you believed in the Vedas (the body of Hindu literature that is considered to be divinely revealed). The bulk of the Vedas is largely incomprehensible to most -- it was composed in an archaic early form of Sanskrit. Partly due to that, there is an incredible diversity in the philosophical schools of thought that claim that their ideas are derived from the Vedas. Only one of these schools of thought are mainstream today -- Vedanta.

Buddhism was deemed a 'nastika' school of thought by the orthodoxy because Buddhism did not acquiesce to the authority of the Vedas. Jainism was also deemed a 'nastika' school of thought for similar reasons. Other faiths that were deemed 'nastika' are no longer widely practiced. The 'astika' school of thought that survived, Vedanta, is extremely similar to Buddhism -- at least as per some of the popular interpretations of it. However, Vedanta acquiesces to the authority of the Vedas, even though sometimes the underlying texts suggest that the acquiescence was nominal or even just out of practicalities (hey, if I claim I acquiesce, the orthodoxy will leave me alone...).

If you look at the development of Hinduism, there seems to have been a distinct Vedic religion that seems more like the ancient Greek religion. Then there is a 'Shramana' tradition -- this seems to be the source of religions like Buddhism and Jainism, and of ideas like reincarnation, dharma (righteousness), moksha/nirvana (liberation), etc. There was, around 2,500 years ago, a time when these two distinct traditions collided. Subsequently, there seems to have been a period of unifying these distinct traditions -- the Bhagavad Gita and the Manu Smriti are key texts that discuss this unification. The Manu Smriti, for example, tries to bring it together by dividing up human life into four sections; one where you learn, one where you're a householder, one where you retreat a bit from social life, and the last where you completely retreat. This incorporated the Vedic tradition of being part of society and fulfilling obligations, and the Shramana tradition of being ascetic and renouncing earthly pleasures.

Of course there were numerous local tiny religions, but this synthesized umbrella seemed to have spread across the subcontinent slowly. As it spread, stories were told that incorporated the local deities to the Vedic deities, and local stories of local deities were used to espouse Shramana ideas. The umbrella itself was of course influenced by this.

Islam and Christianity also seriously influenced Hinduism.

Anyways, my point is that I think, to some extent, something existed that, after going through changes, is what we call Hinduism today. There is some unity and continuity, even if it is far less unified or continuous than other major religions.