How should an aspiring buddhist view or respond to Anti-Buddhism verses from Vedic/Puranic texts?

I find myself frequently drawn towards the philosphy and teachings of the Buddha and feel eager to learn more about it and incorporate it in my life. However, coming from a background where the Vedas and puranas (which are deemed the 5th veda) are held as gospel truth, I often find my faith in the teachings wavering due to my long prior exposure to countless texts from this very background that reiterate again and again that Buddhism is a false philosophy created only for the destruction & delusion of the asuras/demoniacal people. A small sample - Brahmanda purana > 38b-42. Formerly, in the battle between the Devas and the Asuras, **the > Asuras were defeated. They created the heretics like Vṛddhaśrāvakīs, > Nirgranthas, (nude Jainas), Śākyas (Buddhists)**, Jīvaskas and Kārpaṭas. Padma Purana 6.236.5-7 > **Visnu of the form of Buddha proclaimed the false Buddhist doctrine and > those of the naked and wearing dark blue garments for the destruction > of the demons.** The doctrine of Maya (illusion) is a wicked doctrine > and said to be pseudo- Buddhist. I myself, of the form of a Brahmana, > proclaimed it in Kali (age).” Agni Purana 16.1-6 > They sought refuge in the lord saying, “Protect us! Protect us!”. He > (Viṣṇu), who is of the form of illusory delusion became the son of > Śuddhodana. > > 3-4. He deluded those demons. **Those, who had abandoned the path laid > down in the Vedas, became the Bauddhas and from them others who had > abandoned the Vedas. He then became the Arhat (Jaina). He then made > others as Arhats. Thus the heretics came into being devoid of vedic > dharmas.** > > **5-6. They did such a work deserving hell (as reward).** They would > receive even from the vile. All of them became mixed Dasyus and devoid > of good conduct at the end of Kaliyuga. Vishnu Purana III.18.14-26 > **It is known” (Budhyate), these Daityas were induced by the arch > deceiver to deviate from their religious duties (and become Bauddhas), > by his repeated arguments and variously urged persuasions, When they > had abandoned their own faith, they persuaded others to do the same, > and the heresy spread, and many deserted the practices enjoined by the > Vedas and the laws. The delusions of the false teacher paused not with > the conversion of the Daityas to the Jaina and Bauddha heresies, but > with various erroneous tenets he prevailed upon others to apostatize, > until the whole were led astray, and deserted the doctrines and > observances inculcated by the three Vedas**. Some then spake evil of the > sacred books; some blasphemed the gods; some treated sacrifices and > other devotional ceremonies with scorn; and others calumniated the > Brahmans. “The precepts,” they cried, “that lead to the injury of > animal life (as in sacrifices) are highly reprehensible. To say that > casting butter into flame is productive of reward, is mere > childishness. If Indra, after having obtained godhead by multiplied > rites, is fed upon the wood used as fuel in holy fire, he is lower > than a brute, which feeds at least upon leaves. If an animal > slaughtered in religious worship is thereby raised to heaven, would it > not be expedient for a man who institutes a sacrifice to kill his own > father for a victim..." For those who are not from the same background where the vedas and puranas(which are deemed the 5th veda) are held as the paramount truth, it would probably seem like a very trivial issue. A non-issue even. However due to my frequent exposure to such instances, I often find myself mentally torn despite deep inside wanting to follow the Buddha's way. It's as if a part of me is always afraid :- What if these texts are true and buddhism is false? My Question is, As someone who aspires to embrace buddhism, how should I weed out the self-doubt created in my mind from these towards the buddhist philosophy? Please help.