Salvation In Hinduism

1. No salvation for practising anything opposite to the Vedas

📚Shrimad Bhagavatam 6.1.40📚
The Yamadūtas replied: That which is prescribed in the Vedas constitutes dharma, the religious principles, and the opposite of that is irreligion. The Vedas are directly the Supreme Personality of Godhead, Nārāyaṇa, and are self-born. This we have heard from Yamarāja.”  (source)

📚Narada Purana 1.41.106📚
It is only through the repetition of the names of Hari that redemption is attained by the people who commit sins, who are beyond the pale of Vedic path and who are wanting in mental purity.”  (source)

2. Atheists cannot get salvation

📚Shrimad Bhagavatam 7.1.32📚
Somehow or other, one must consider the form of Krsna very seriously. Then, by one of the five different processes mentioned above, one can return home, back to Godhead. Atheists like King Vena, however, being unable to think of Krsna’s form in any of these five ways, cannot attain salvation. Therefore, one must somehow think of Krsna, whether in a friendly way or inimically.”  (source)

📚Skanda Purana 5.3.227.1-4📚
Thus, succinctly and in accordance with their importance these Tīrthas have been recounted to you. O son of Pāṇḍu, no one is competent to enumerate in detail all the Tīrthas. This river Narmadā is sacred and pure. It is well-known in all the three worlds. She is the most excellent of all the rivers, and a favourite of Mahādeva. If anyone always remembers mentally and reflects on Narmaḍā, O king, he obtains quickly the excellent benefit of a hundred Cāṇḍrayaṇas. Persons who have no faith, those who are atheists fall into the terrible Naraka. So said Parameśvara.”  (source)

📚Vamana Purana 40.35-36📚
Therefore Dharma is not to be shunned, for Dharma is the supreme goal. Men devoid of Dharma go to the wide Raurava hell. “Dharma, they say, enables safe passage in heaven and here and Adharma leads to downfall in this world and the next.”  (source)

📚Kurma Purana 2.19.31-32📚
If any Brahmana does not practise his duty either due to atheism or due to lethargy, he falls into the terrible hells and is reborn as a crow. There is no other way for liberation excepting performance of the duties of one’s own Asrama (stage of life). Hence one should perform the holy rites for the satisfaction of Paramesthin (god-Brahma).”  (source)

📚Kurma Purana 2.24.7📚
Either due to atheistic feelings or due to lethargy, if anyone does not wish to maintain sacrificial fires, nor does he perform Yajfias, he falls into many hells.”  (source)

📚Narada Purana 1.15.79-80📚
I shall tell you the sufferings of the atheists who turn their faces away from Hara and Hari. They will be compelled to eat salt for ten million years. Then, they are scorched and fried in red hot sand in Raurava hell. These men of sinful acts remain in that hell for the period of a Kalpa. O ruler of men, in other hells also (they are tortured) like this.”  (source)

📚Shrimad Bhagavatam 11.5.15📚
The conditioned souls become completely bound in affection to their own corpselike material bodies and their relatives and paraphernalia. In such a proud and foolish condition, the conditioned souls envy other living entities as well as the Supreme Personality of Godhead, Hari, who resides in the heart of all beings. Thus enviously offending others, the conditioned souls gradually fall down into hell.”  (source)

📚Skanda Purana 5.2.67.23-31📚
a voice issued from the firmament as uttered by me in compassion: “Do not say anything out of the way. The immutable Śrutis should not be censured. The Purāṇas spoken by Brahmā, the creator of the worlds, cannot be otherwise. The atheists who censure the Purāṇas and Dharmaśāstras fall into the terrible hell and remain there till all the living beings are annihilated.”  (source)

📚Skanda Purana 7.1.3.144📚
Thus the foolish ones will say, others will laugh. The non-beleivers, the people destined to fall into hell, get their minds overwhelmed by sins. At the advent of Kali Age, they will never gain Siddhi.”  (source)

📚Linga Purana 2.11.35-37📚
If people forsake Linga and begin to worship other deities they will go to the Raurava hell along with the king, their ruler. If a king ceases to be a devotee of Siva and becomes attached to other Devas, it is like the behaviour of a young woman who discarding her husband revels among her paramours.”  (source)

📚Kurma Purana 1.12.259-261📚
The hells such as Tamisra and others were created beneath the earth by god Brahma for those people who do not practise the duties prescribed in my Dharma. There is no scripture other than the Vedas which lays down what is Dharma. A person who takes delight in other things (not sanctioned by the Vedas), should not even talked to by twice-born persons viz. Brahmanas, Ksatriyas and Vaisyas. Those various scriptures which are contrary to Srutis and Smrtis seen in this world, are based on Tamo-guna or ignorance. Belief in them or practising in accordance with them is a Tamasa activity.”  (source)

📚Padma Purana 5.96.49b-76a📚
Those men who are averse to religion through their deeds, mind and words, and who are without (i.e. who do not have) devotion to Viṣṇu, go to hell. Those men who look upon Brahmā, Śaṅkara and Viṣṇu as different (from one another), and who are detached from knowledge about Viṣṇu, go to hell. That man who, through lust or delusion, gives up the act proper for his family or country, and would do something else, goes to hell. A man who worships what should not be worshipped, and does not worship what should be worshipped, and is disinterested in the knowledge about Viṣṇu, suffers in many hells.”  (source)

📚Brahma Purana 65.71-73📚
Thus O brahmins is the greatest abode of Visnu endowed with all enjoyable pleasures and attributes. It is conducive to the pleasures of everyone. It is holy and full of mysteries. Atheists and profligates do not go there. Nor do the following go there viz.-the ungrateful and those who are of uncontrollable sense-organs. The devotees of Visnu who worship Vasudeva the preceptor of the universe with devotion, go to the world of Visnu.”  (source)