It is surprising that a question like this would be so controversial and get answered in so many ways. The first impression I would imagine most people would have is of course it is a religion, it is formally recognised as a religion - the third largest in the world as a matter of fact - and it is so obvious it is a religion because it worships god/s. Alternatively, if the question was asked “Is Yoga a religion” most people’s first impressions are it is not a religion, it is a science, which just happens to come from the Hindu tradition. So if we go by first impressions: Hinduism = religion and Yoga = science.
Now the more interested amongst us who do not take first impressions and answers for granted, would do a little more research and it will become plainly obvious Yoga is identical to the essences of Hinduism. This will be born out by the fact that the philosophy of Yoga and the practices of Yoga is the philosophy of Hinduism and the practice of Hinduism. Therefore this means either that Hinduism is a science or Yoga is a religion? If Yoga is Hinduism and Yoga is a science, then Hinduism is a science. If Hinduism is a religion and Yoga is Hinduism, then Yoga is a religion. Which one is true?
I was watching an excellent discourse by swami Mukundananda, where he is giving a talk at the Kellogs business school, apparently one of the most prestigious business schools in the world. His talk is on spirituality and management. In an answer to a question on the differece between spirituality and religion, he says that spirituality is non-secetarian and universal, it is applicable across cultures and historical periods. Indeed that is what Hinduism purports to be - sanatana dharma - the way of the eternal or the knowledge of the essential nature of reality. In which case this means Hinduism is pure spirituality and hence a science.
If religion is understood as faith and a set of dogmas, then Hinduism most definitely cannot be a religion. Many say, and I was reading the abstract of an article in the Oxford University press echoing the same, that Hinduism as a religion is a modern colonial invention. In order to understand dharmic culture more coherently the West had to classify it under their framework, but later Western scholars of Hinduism would actually find this classification to be highly controversial, because Hinduism does not fit any of the major categories of religion, philosophy or science neatly. In fact the tradition itself does not have an equivalent words or concepts for these Western categories. The closest are: dharma for religion, but dharma means way/essential nature or order of something; darshana for philosophy, but darshana means a viewpoint or vision of reality; and the closest to science is vidya, but vidya means any kind of systematic knowledge including metaphysics and spirituality. Moreover, the Indian scientific method is a pure epistemology and not exclusively empirical.
Thus the question needs to be posed do we really need this term Hinduism when it is proving to be so problematic and become a liability for Hindus today or must we keep it to ensure that we retain our cultural integrity?