In Buddhist philosophy, Realism is often attributed to the Sarvāstivāda school. See, for instance, the expressions “Realismus des Sarvāstivāda” and “den primitiven Realismus des Sarvāstivāda” in Frauwallner 1956: 119. Perhaps it is useful to bear in mind that there are “various kinds of realism, e.g. realism about physical/material things, about scientific entities, about mathematical objects, about the past” (Matilal 1986: 15, referring to Dummett). We are concerned only with the physical/material/external entities/objects (bāhyrārtha: phyi rol gyi don). Bimal Matilal also points out that “we are concerned with two specific claims: a claim about the existence of these objects, another claim about the nature of that existence.” He goes on (Matilal 1986: 15): “In fact the two claims must go together. Otherwise the dispute between realism and phenomenalism will disappear. For realism, the familiar physical object not only exist but also exist independently. This crucial expression ‘independently’ means that by chance all the sentient creatures were annihilated our familiar physical objects would still continue to exist in the same way. Phenomenalism disputes this claim: the familiar objects exist but not independently of any sentient creatures’s being aware of them. If all ‘minds’ were annihilated it would not only be pointless but also false claim that a certain set (any set) of entities existed.” This explanation seems to make the use of the term “realism” in the Indian philosophical context very clear.
Nonetheless, I am afraid that if we understand “Realism” as a philosophy which posits an independent existence of physical/material/external entities, we can no longer speak of “Buddhist realism” at all, that is, not only because of the use of the expression ‘independently,’ which I understand here not as ‘independently of causes and conditions’ but as ‘independently of perceptual/conceptual cognition.’ Bimal Matilal’s definition of “realism” is narrow and applies only to what he calls “Nyāya Realism” and our Sarvāstivāda Realism (here) would not fulfil the criteria of his “realism” and is to be subsumed under what he calls “Buddhist/Abhidharma Phenomenalism.” In the Buddhist context, it is perhaps felicitous to (re)define “Realism” as a philosophy according to which external/physical entities not only exist but exist really/substantially (dravyasat: rdzas su yod pa), that is, regardless of whether these external entities are dependent or independent of perceptual/conceptual cognition. Realism in this sense concern two issues: existence of external entities and the ontological status of these entities. Epistemic issues, though related, is not decisive here. In other words, I define “Realism” purely from an ontic/ontological perspective and not from an epistemic/epistemological perspective. As such the questions are whether, which, and how (i.e. substantially or nominally) external entities exist, and not so much as to whether and how they are perceived or cognised. While we can anticipate a consensus among the various Buddhist philosophical systems on the existence of external entities such as visible/material objects (rūpa: gzugs), there is bound to rule dissensus among them regarding their real/substantial or unreal/nominal existence (prajñaptisat: btags par yod pa). Following this (re)definition of “Realism,” we could speak of Vaibhāṣika Realism and Sautrāṇtika Realism, insofar as both Vaibhāṣika and Sautrāntika systems are said to posit the real/substantial existence of external entities.* There is bound to be a wide range of Yogācāra and Madhyamaka positions on the ontological status of the external entities.
*Rong-zom-pa, Grub mtha’i brjed byang (p. 199.1–2): bye brag pa dang mdo sde pa gnyis ka ’dra bar yul rdul phra rab rdzas su yod par ’dod do ||.