In the MN 95, the Buddha hints that even the learned brahmans themselves are unsure whether the Vedas are true, by their own empirical validation:
"And among the brahman seers of the past, the creators of the hymns,
the composers of the hymns — those ancient hymns, sung, repeated, &
collected, which brahmans at present still sing, still chant,
repeating what was said, repeating what was spoken — i.e., Atthaka,
Vamaka, Vamadeva, Vessamitta, Yamataggi, Angirasa, Bharadvaja,
Vasettha, Kassapa & Bhagu: was there even one of these who said, 'This
we know; this we see; only this is true; anything else is worthless?'"
"No, Master Gotama."
"So then, Bharadvaja, it seems that there isn't among the brahmans
even one brahman who says, 'This I know; this I see; only this is
true; anything else is worthless.' And there hasn't been among the
brahmans even one teacher or teacher's teacher back through seven
generations who said, 'This I know; this I see; only this is true;
anything else is worthless.' And there hasn't been among the brahman
seers of the past, the creators of the hymns, the composers of the
hymns... even one who said, 'This we know; this we see; only this is
true; anything else is worthless.' Suppose there were a row of blind
men, each holding on to the one in front of him: the first one doesn't
see, the middle one doesn't see, the last one doesn't see. In the same
way, the statement of the brahmans turns out to be a row of blind men,
as it were: the first one doesn't see, the middle one doesn't see, the
last one doesn't see. So what do you think, Bharadvaja: this being the
case, doesn't the conviction of the brahmans turn out to be
groundless?"
MN 95
In MN 95 and DN 13, the Buddha did not accept the authority of the Vedas. This makes Buddhism a heterodox (nāstika) school.
In Dhp 279 and many other suttas, the Buddha taught all phenomena is not self. This also makes Buddhism a heterodox (nāstika) school.
In MN 38, he taught six types of consciousness which dependently arise based on the six media of eyes, ears, nose, tongue, body and mind i.e. eye-consciousness, ear-consciousness, mind-consciousness etc. He taught that consciousness does not occur independently of these six media. This disagrees with the concept of Cosmic Consciousness (Aparokshanubhuti 58) in Advaita Vedanta.
In SN 7.9, he rejected the notion of varna/ caste by birth, stating "don’t ask about birth, ask about conduct," when someone asked him about his (Buddha's) varna/ caste at birth. That contradicts Chandogya Upanishad 5.10.7 and BG 9.32.
In SN 7.7, he said that austerities does not make one pure and chanting mantras do not make one a brahmin, stating instead that accomplishment in conduct or virtue, and knowledge determines a brahmin.
In SN 7.21, he rejected the view that purification rites using water can wash away sins, stating instead to dip oneself in the shores of the lake of virtue, to purify oneself.
In DN 31, he rejected the ritualism behind the Vedic bath prayer ceremony practised by a young householder by the name of Sigala and put a new spin on it.
In MN 92, the Buddha stated that feeding the Sangha generates more merit than the Vedic fire sacrifice (yajna), while AN 9.20 states that undertaking the five precepts generate more merit than feeding the Sangha.
In SN 42.6, he rejected the use of funeral rites to help the deceased go to heaven, stating instead that it is a person's deeds during their lifetime which determines their outcome, and not rituals performed after death.
In SN 42.3, he rejected the view that a warrior performing his duty to fight in war, will allow him to go to heaven after death, if he gets killed in battle. This contradicts BG 2.38.
In AN 8.39, he forbade taking of a life and in AN 4.39, he denounced animal sacrifices. This may have conflicted with animal sacrifices that may have been practised in his time.
In DN 2, he forbade his monks from doing fire oblations or fire sacrifices, practising astrology, reading omens, interpreting dreams, calculating auspicious dates for marriages, consecrating sites for construction and worshipping the Sun etc.