There is a superficial understanding of Hinduism as a polytheistic religion that worships a pantheon of gods and goddesses using idols as its primary means. This is the understanding of people who are not very learned in Hinduism.
Then there is a learned and considered understanding of Hinduism, as a henotheistic philosophy that worships a single god using multiple methods, but that is manifest in infinite forms. This is also found in the Rig Veda, “Truth is one, and the wise call it by name names” There are 330 million of these forms recognised by Hindus, and of these 330 million forms the principal forms are Shiva, Vishnu, Duga, which respectively are the deities of the three main traditions of Hinduism: Shivaism, Vaishvaism and Shaktism. All traditions accept several methods of worship: tantra, yantra, yoga, mantra, idol worship and accept several scriptures agamas, shastras, puranas, vedas. It will become clear then Hinduism is not defined by any particular diety, methods or ways, any scripture or founder, or language. Thus Hinduism has no problem embracing the deities, methods or scriptures of any other religion. If a Hindu wanted to accept Jesus as their deity, Hinduism would have no problem with this. In fact Hinduism has the concept of Ishtadevata which means one can choose any object of worship of their choice, even a living person if they wish.
How Hinduism is defined is by its genera philosophy which all Hindu traditions embrace. That is dharma, karma, reincarnation and yoga. Dharma is eternal laws and principles that one should live in harmony with; karma is the law of cause and effect; reincarnation defines ones goal in life as to escape the cycle of birth and rebirth and yoga is any kind of valid technique through which one can attain to the utimate goal of moksha/salvation. These in turn are based on the Upanishadic and Dashana philosophy(aka Vedic or Hindu phiosophy)
It is called Indian philosophy when you are dealing with both Hindu philosophy and Buddhist, Jain and other non-vedic philosophies. But if you are only dealing with the Darshanas, then it is called Hindu or Vedic philosophy. The division between Vedic and non-vedic philosophy is known as astika and nastika(orthodox and non-orthodox) If they are combined together, they are given the secular term, “Indian philosophy”
So it should become clear now Hinduism is its philosophy. More correctly understood, it is a philosophical religion. It is based on generals, not particulars. It does not matter which deity you worship, which scriptures you read, which method you use in Hinduism, this is why there is so much pluralism. What does matter is the core philosophy which is there is a sef, which is infinite and the source of all that is good, and it is our goal in life to realise the sef, and we can use anything that helps us in this journey.
If you believe in reincarnation, eternal laws, cause and effect, chakras, meditation, mantra, yoga, astral planes you are adopting Hindu beliefs. However, they are no more beliefs, than the law of gravity is a belief. These are truths that one will discover in any valid spiritual tradition.
