The main principles of Hinduism all depend on reincarnation. From reincarnation, Karma becomes meaningful, and so do all the prescriptive practices given in the Vedas, Upanishads, and other scriptures. Reincarnation and Karma are the basis and justification for the Caste System - a major historical part of Hinduism and Indian society. And, the entire goal of Hinduism itself is ultimately to escape the cycle of reincarnation (Samsara).
However, similar to how most Catholics don't know, or care, about Catholic doctrine, only 40% of Hindus surveyed by Pew Research in India said that they believe in reincarnation.
Such are not only in a false religion, but are not even consistent with the false religion that they operate under. What is the point of identifying with a religion whose core tenets you don't even believe in? Worse, they raise their children in this religion.
And, lest there be any doubt about whether Hinduism teaches reincarnation, what follows are quotes from the Ten Principal Upanishads - which are part of the Vedic corpus of texts that are the foundation for nearly all sects of Hinduism - teaching exactly that:
Katha Upanishad - Book 1, Chapter 3
7 If the buddhi, being related to a distracted mind, loses its discrimination and therefore always remains impure, then the embodied soul never attains the goal, but enters into the round of births.
8 But if the buddhi, being related to a mind that is restrained, possesses discrimination and therefore always remains pure, then the embodied soul attains that goal from which he is not born again.
Katha Upanishad - Book 2, Chapter 1
10 What is here, the same is there and what is there, the same is here. He goes from death to death who sees any difference here.
11 By the mind alone is Brahman to be realised; then one does not see in It any multiplicity whatsoever. He goes from death to death who sees multiplicity in It. This, verily, is That.
Katha Upanishad - Book 2, Chapter 3
2 Whatever there is - the whole universe - vibrates because it has gone forth from Brahman, which exists as its Ground. That Brahman is a great terror, like a poised thunderbolt. Those who know It become immortal.
3 From terror of Brahman, fire burns; from terror of It, the sun shines; from terror of It, Indra and Vayu and Death, the fifth, run.
4 If a man is able to realise Brahman here, before the falling asunder of his body, then he is liberated; if not, he is embodied again in the created worlds.
Prashna Upanishad - Chapter 1
9 The year is the Creator. There are two paths, the southern and the northern. Those that are content with alms-giving and ritual preferring the life of the family, go to their ancestors by the southern path, attain the lunar world and are born again. All there is matter.
Prashna Upanishad - Chapter 3
9 When a man dies, his person loses fire, as fire is the element (breath) that upward ascends; All the organs then enter into his mind, and through rebirth the man again descends.
Prashna Upanishad - Chapter 5
1 Satyakama Shaibya asked: "Lord! Where does the man go after his life, if he meditates on Om all his life?"
2 The Sage said: "Om is the conditioned and the unconditioned Spirit. The wise man with its help alone attains the one or the other.
3 If he meditates on the syllable A alone he is soon born again on this earth. If he has chanted the Rig Veda, he is born among men, a great, austere, self-controlled, God-fearing man.
4 If he meditates on the two syllables A and U, and has chanted the Yajur Veda, he goes to the moon and, after enjoying its pleasure, returns to the earth again and again.
Mundaka Upanishad - Book 1, Chapter 2
7 All the sacrifices performed by the eighteen people connected with them are transient and unsafe boats in crossing this Samsara. These actions are inferior. Those ignorant ones who glorify and consider as good these actions go to birth and death again and again.
8 Drowned in the midst of ignorance, but thinking themselves great and learned, the deluded ones, attacked from all sides by decay, disease and death and several other miseries, turn round and round in the wheel of Samsara like blind men guided by blind men.
Mundaka Upanishad - Book 3, Chapter 2
1 Him who knows this Supreme Abode of Brahman in which the whole universe is situated and which is brilliantly shining, those heroes who adore and worship, without any desire in their minds, transcend this seed of birth.
2 He who contemplates on objects of desire, having a desire for them, is born here and there due to those desires; but for him whose desires are all fulfilled, whose Self is perfectly contented due to the sense of perfection, all desires dissolve themselves here itself.
Chandogya Upanishad - Book 4, Chapter 15
5 'Now, as for such persons, whether the cremation rites are performed or not, they go to light; from light to the day; from the day to the bright fortnight; from the bright fortnight to those six months during which (the sun) rises towards the north; from the months to the year; from the year to the sun; from the sun to the moon; from the moon to the lightning. (From the region of Brahman) a person, who is other than human, (comes and) causes them existing there, to realize Brahman. This is the path of the gods and the path to Brahman. Those who go by this path do not return to this human whirlpool - yes, they do not return.'
Chandogya Upanishad - Book 5, Chapter 10
7 Among them, those who did good work in this world [in their past life] attain a good birth accordingly. They are born as a brāhmin, a kṣatriya, or a vaiśya. But those who did bad work in this world [in their past life] attain a bad birth accordingly, being born as a dog, a pig, or as a casteless person.
Chandogya Upanishad - Book 8, Chapter 6
6 There are a hundred and one arteries leading to the heart; one of them pierces the crown of the head. He who goes upwards through it, attains immortality; He who does not, is born again.
Brihadaranyaka Upanishad - Book 4, Chapter 4
When body grows weak through age or disease, the Self separates itself from the limbs, as a mango, a fig, a banyan fruit separates itself from the stalk; man hastens back to birth, goes, as before, from birth to birth.
As a caterpillar, having reached the end of a blade of grass, takes hold of another blade, then draws its body from the first, so the Self having reached the end of his body, takes hold of another body, then draws itself from the first.
And as a goldsmith takes the gold from an old piece of jewelry and shapes it into a more modern piece, so the Self forgets the old body, takes hold of another body, whether like that of the fathers, or of the celestial singers, or of the gods, or of the begetter, or of any other creature.
This Self is Spirit. He is knowledge, mind, life, sight, hearing, earth, water, wind, air, light, darkness, desire, absence of desire, anger, placability, right, wrong; He is everything; He is this and that. Whatever his conduct and character in one life, he has it in his next; if good in one, he is good in another; if a sinner in one, he is a sinner in another; his good karma makes him good, his sinful karma makes him sinful.
Hence they say that soul is full of desire. He wills according to his desire; he acts according to his will; he reaps what he sows. Here is my authority: "Self goes where man's mind goes. Whatever his actions in this world, he enjoys their reward in the next; that over, he returns for action's sake. I speak of a man with desire; but what is he who has no desire? He has no desire, because he has attained his desire; desire of Self is no desire. He does not die like others; he is of Spirit, he becomes Spirit."
Brihadaranyaka Upanishad - Book 6, Chapter 2
15 Those who know this as such, and those others who meditate with faith upon the SatyaBrahman in the forest, reach the deity identified with the flame, from him the deity of the day, from him the deity of the fortnight in which the moon waxes, from him the deities of the six months in which the sun travels northward, from them the deity identified with the world of the gods, from him the sun, and from the sun the deity of lightning. (Then) a being created from the mind (of Hiranyagarbha) comes and conducts them to the worlds of Hiranyagarbha. They attain perfection and live in those worlds of Hiranyagarbha for a great many years. They no more return to this world.
16 While those who conquer the worlds through sacrifices, charity and austerity, reach the deity of smoke, from him the deity of the night, from him the deity of the fortnight in which the moon wanes, from him the deities of the six months in which the sun travels southward, from them the deity of the world of the manes, and from him the moon. Reaching the moon they become food. There the gods enjoy them as the priests drink the shining Soma juice (gradually, saying, as it were), ‘Flourish, dwindle’. And when their past work is exhausted, they reach (become like) this ether, from the ether air, from air rain, and from rain the earth. Reaching the earth they become food. Then they are again offered in the fire of man, thence in the fire of woman, whence they are born (and perform rites) with a view to going to other worlds. Thus do they rotate. While those others who do not know these two ways become insects and moths, and these frequently biting things (gnats and mosquitoes).
Religious apathy is frustrating, because a person's beliefs about religion affect everything that they do, and also affects their entire family, and society as a whole. I do not understand why anyone would identify with a religion whose core teaching they don't even believe.