Please post a poll showing that majority of Hindu-s believe that these are the core beliefs (not popular beliefs but essential beliefs) and one cannot be a true Hindu if they do not believe them.
I don't think you honestly understand what a 'darsana' is, though you are always talking about the darsanas here. A darsana is a
system of philosophy, this is how the words usually translated. Now, because it is a system, the matrix of beliefs within that system interconnect with one another, such that you cannot reject one core belief without rejecting several others.
A darsana is a complete system of philosophy which covers every major area of philosophy: Epistemology(pramana), Metaphysics(tattva), Cosmology(shrishti) Ethics(achara) and Soteiology(moksha) In this order. First the means of knowledge are established, because this is how we know how we know whatever they know; second, through that epistemology, the categories of knowledge are established to make up the "element" of that system; third a cosmology is established in which order or sequence the tattvas come; Then a system of ethics is developed on how one should live and finally the means to liberation.
There are several systems developed which deal with specific areas of study:
Vaiseshika: Vaiseshika deals with the subject of the real world of experience. It is based on using perception to analyse all the categories that make up the real world, hence the elements of the system are taxomonic(such as substance, qualities, actions etc) but this is done for the sake of it, it is done as the first sutra itself declares, to analyse the dharma of everything that exists so that knowing which one can know the right action to do and attain supreme happiness.
Nyaya: Nyaya deals with the subject of epistemology. It is based on analysing meaning the structure of inference and hence the elements of the system are all logic based (re means of knowledge, objects of knowledge) However, it is again not for its own sake, it is so that one can correctly attain discirminative knowledge.
Nyaya-Vaiseshika form a single pair because they share the same objective of correctly understanding the world we live and removing errors of understanding. Their main emphasis is to convince that we are not the body, that there is a soul which transmigrates from body to body carrying merit or demerit, and evolving gradually. The emphasis is to correct us to right thinking and right action so we evolve.
Samkhya: Deals with the subject of the structure of experience. It is based on analysing structure of experience for which there is an experiencing subject and an object which is experienced and instruments for which they are experienced(re: 5 senses, mind, ego, intellect etc) This is too not done for its own sake, it is so that the soul is released from all kinds of pain and attains its true nature(again declared in first sutra)
Yoga: Yogs is just the praxis aspect of Samkhya, it analyses the practice of meditation. It analyses what meditation should consist of(re yama, niyama, asana, pranayama) by which the goal of cessation of all pain of Samkhya is achieved.
Samkhya-Yoga form a single pair because they share the same objective of teaching the knowledge by which we are releaed. While, Samkhya explains to us the theory on how we cease all suffering and gain release from the cycle. Yoga is the practice by which it is achieved.
Purva Mimamsa: This studies the karma khanda of the Vedas. It reveals with the devas/gods, the controlling powers that control this universe, and how we can invoke these powers through the power of ritual to obtain whatever we desire.
Uttara Mimamsa: This studies the jnana khanda of the Vedas or the concluding teaching of the Vedas(Vedanta) which reveals Brahman as the supreme Lord and supreme reality and its relationship with us Atman. It reveals our ultimate goal to realise the Brahman in our Self, to either mege with Brahman, attain oness with Brahman or rejoin Brahman.
Purva Mimamsa and Uttara Mimamsa form a single pair because they share the same objective of exegesis of the Vedas. They accept testimony of the Veda as their main means.
Altogether these 6 systems form a complete system which we know as the Vedic religion or HInduism. They are not opposing, but complimentary. I actually must laugh, you find Buddhism, Jainism, Hinduism and Charvaka as some single complimentary "dharma" despite the fact that they are mutually opposing and contradict one another. On the other hand, you view the six systems of Hindu philosophy as opposing despite they mutually compliment one another and link one another. None of them contradict the Veda. Samkhya accepts the means of knowledge of Pramana from Nyaya; Vaiseshika accepts the 5 elements of the Samkhya and further defines the tanmatras as atoms and goes into details on how they combine; Nyaya accepts the means of release of Yoga. They all accept moksha as the final goal(summon bunnom)
This is why scholars consider them systems of thought of a single Vedic dharma, and not consider them separate from it, as they do with Jaina, Buddha and Charvaka. So now that I have explained this, I can show you how we piece together the entire system
Epistemology: We accept the Rishis as the founders of our religion and hence their testimony is Word for us. All Smriti literature, such as Bhagvad Gita, Agamas and Tantra must agree with Veda we reject it. The Rishis are our Prophets and you cannot reject anymore a Christian can reject Jesus, a Buddhist Buddha, a Muslim Mohammed.
Metaphysics: Whether you accept the 24 tattva scheme of the Samkhya or the 36 Tattva scheme of Shaiva, the following are common in all of them: 5 subtle elements, 5 gross elements, 5 sense organs, 5 action organs, discriminating mind, ego and intellect, soul and nature. In addition we accept Ishvara, Maya and Brahman. The 36 tattva scheme is basically the same scheme but with Ishvara and Maya further divided into 5 aspects each
Cosmology: We accept that Brahman is the supreme being that has created this universe using his creative power of Maya and enters into it as trimurti as creator(Brahma) preserver(Vishnu) and destroyer) this creates the entire universe and all its regions and lokas. The avidya aspect of Maya deludes the jivas causing the first fall from grace, they either separate from Brahman, or leave Brahma abode or are Brahman themselves forgetting their original nature. This plunges the jiva to take repeated births in the universe, circling through the regions.
Ethics: We accept that the Jiva's transmigration is governed by the law of karma which in turn based on dharma. If we do our dharma correctly, the law of karma produces merit, if we do it incorrectly, it produces demerit. The merit or demerit that attaches to the jiva, taking it up and down the regions of samsara. Good karma to higher regions, bad karma to lower regions. It also decides the body they inherit and its aptitudes. This is further divided into a four-fold vision a mere labourer(a slave, a servant) a merchant(landowner) a warrior(king) or a sage. The Jiva must gradually through several lifetimes become a sage. In order for it do so, it must fulfil the first three goals of life kama, artha and dharma before it seeks moksha.
Soteriology: The release of the Jiva from samsara is for the jiva to gain knowledge, because action will only move it up and down samsara, but not release it from Samsara. It must realise it is not any of the multitude of bodies it has(gross, suble and causal) and it must detach from identification with the bodies and redirect all its desire to Brahman to win Brahman's grace. It must have a yearning desire for Brahman in whichever form it chooses to relate to Brahman or with whatever emotion(servant, friend, father, mother, teacher, child etc)
This is the Hindu darsana. The Hindu system. An extremely well developed and comprehensive system build up from premise to conclusion. How can I accept you as a Hindu if you reject our entire system? You reject our epistemology, you reject our metaphysics, you reject our cosmology, you reject our ethics and you reject our soteriology? You even reject our history(the solar and lunar dynasties, Krishna, Mahabharata)
How can I be Buddhist if I reject the four noble truths?
How can I be Charvaka if I reject materialism?
How can I be vegetarian if I reject eating vegetarian food?
I am sorry but it is not me imposing my beliefs on you. I am just the messenger and you are shooting the messenger. I am merely somebody who is pointing out to a vegetarian that they are not vegetarian if they eat meat. You can hate me for it all you want. It might make me unpopular with a lot of people -- but is the truth and I go with the truth.