My recollection of John Peacock’s view was that he believes the main impact of Brahmanism on Buddhism occurred after the Buddha’s time, and that the texts thus sometimes show the impact of a later “creeping Brahmanism”. Johannes Bronkhorst’s recent book argues that the primary context in which the Buddha’s teaching emerged was not among the Brahminified region to the west, but in the region of “Greater Maghada” among the various samana schools of that region, particularly the Jains and Ajivikas.
But I think it is important to recognize that there are Brahmins everywhere in the Sutta Pitika. Sometimes these interactions are portrayed as antipathetic, but other times as quite respectful. One of the most important of the early texts, the Pārāyana Vagga of the Sutta Nipata, consists entirely of conversations between the Buddha and 16 Brahmin students, who following the directions of their teacher Bavari traveled to the Buddha to question him and learn from him as a revered teacher of renown. The commentary says that Bavari was a Brahmin ascetic, and that the students were all converted. The tradition also informs us that Sariputta was a Brahman, Moggalana was a Brahman and Kassapa was a Brahman. And the Buddha deliberately selected these people as his chief disciples, which is in itself and interesting clue.
My interpretation is that the Buddha saw himself as carrying out a kind of “mission” to the Brahmas, not to convert them to an entirely new way of thinking, but to call them back to what he regarded as a purer, more austere, and more ancient and original renunciant tradition that had existed among them. He’s a Kattiyya acting at the same time as a kind of reforming Brahmanic puritan. (Maybe one reason he was so interested in getting prominent Brahmin disciples was to learn more about Brahminic teachings from them, teachings he had not picked up himself in his wanderings.) The Brahmins in the Suttas are often represented as responding favorably to this teaching, and so it seems safe to assume there was already quite a bit of internal debate among them about what makes somebody a “true Brahmana” - whether it was purely a matter of birth and ancestry, or more a question of piety, austerity, fidelity to ancestral ways, knowledge of the Vedas, and other personal merits.
The hostility seems to occur with wealthier householder Brahmins who have reached a prominent social position something like a feudal landlord. They are the ones portrayed as mocking and berating “shavelings” and deploring the practice of begging for food rather than working a field to grow it. But even some of these Brahmans are represented as being converted. No doubt there was some growing social resentment toward people who had grown rich and lordly through priestcraft, including among humbler Brahmans themselves, and this had something to do with the spreading popularity of Buddhism.
As we know, the Buddha frequently uses the term “brahman” as a general term meaning something like “holy man” or “one devoted to the holy life”. For example, when the converted Angulimala is hit with a potsherd and a stone, the Buddha tells him, “Bear with it brahman!” There is a common contemporary tendency to say that the Buddha uses the term mainly in an ironical and humorous way to get in a “dig” at the brahmins. But the texts give us the impression that the Buddha is often quite in earnest about using it to refer to “true” brahmins, and that his attitude resonated among a not insignificant number of brahmins themselves. Historians tell us that the caste system had not yet fully emerged as a biologically determined social order in the Buddha’s time. So the Buddha’s teaching took place in a context in which these questions of hierarchy, holiness and social place were still contested - not just among those outside the emerging brahmin caste but within it as well.
The Buddha often call all religiously inclined wanderers and holy men by the single term “samanabrahmana”, which suggests to me he thought of himself as attempting to unify two diverse spiritual traditions into one proper conception of the holy life. And again, this deliberate syncretism probably had something to do with Buddhism’s great success as a movement.
And then there is that whole business of the mahapurisa and the 32 marks! … which suggests the Buddha came to be seen by at least some Brahmins as the fulfillment of an ancient tradition prophesying the appearance of the Great Man.
The Buddhist historiographical tradition often seems to want to make the Brahmins the bad guys pure and simple, or to blame them for all of the distortions in the Buddhist teachings as they have come down to us. But I think the texts point at a more complicated story that we still don’t understand well, especially given the lack of written documents.