Certainly we may say Buddhism is deeper than any philosophy. It is a religion after all.
Regardless, it has teachings about reality and perception. If we are to define “realist” as its most fundamental form, it is surely fair to say it is the position that external reality is mind independent. Theravada fits this definition.
Here is respected Theravada scholar Karunadasa speaking about this issue:
What emerges from this Abhidhammic doctrine of dhammas
is a critical realism, one which (unlike idealism) recognises
the distinctness of the world from the experiencing subject
yet also distinguishes between those types of entities that
truly exist independently of the cognitive act and those that
owe their being to the act of cognition itself.
-Y. Kunadasa, The Dhamma Theory, page 38
dhamma theory is best described as dhamma realism
-The Theravada Abhidhamma: Inquiry into the Nature of Conditioned Reality
By Y. Karunadasa, chapter 2
This theory ensures that the object of direct and immediate
perception is not an object of mental interpretation but something that is
ultimately real.
-Karunadasa, Y. Buddhist Analysis of Matter, pp. 149.
Thus the Theravādins were able to establish the theory
of direct perception of the external object despite their recognizing the
theory of momentariness.
-Karunadasa, Y. Buddhist Analysis of Matter, page 146
"If we base ourselves on the Pali Nikayas, then we should be compelled to conclude that Buddhism is realistic. There is no explicit denial anywhere of the external world. Nor is there any positive evidence to show that the world is mind-made or simply a projection of subjective thoughts. That Buddhism recognizes the extra-mental existence of matter and the external world is clearly suggested by the texts. Throughout the discourses it is the language of realism that one encounters. The whole Buddhist practical doctrine and discipline, which has the attainment of Nibbana as its final goal, is based on the recognition of the material world and the conscious living beings living therein.
Karunadasa, Y. Buddhist Analysis of Matter, pp. 14, 172
Some sutta quotes:
“If, friends, internally the eye is intact but no external forms come into its range, and there is no corresponding conscious engagement, then there is no manifestation of the corresponding section of consciousness. If internally the eye is intact and external forms come into its range, but there is no corresponding conscious engagement, then there is no manifestation of the corresponding section of consciousness."
-MN 28
“Bhikkhus, consciousness comes to be in dependence on a dyad. And how, bhikkhus, does consciousness come to be in dependence on a dyad? In dependence on the eye and forms there arises eye-consciousness.:
-SN 35.93
A given instance of perceptual consciousness is said to arise only in dependence upon two conditions: the sense organ and its corresponding object-field. This implies that perceptual consciousness arises only in conjunction with an appropriate and existent object; perceptual consciousness of a nonexistent object or without an object is, therefore, impossible.
-Disputed Dharmas
Early Buddhist Theories on Existence
An Annotated Translation
of the Section on Factors Dissociated from Thought
from Sanghabhadra’s Nyayanusara
Collett Cox
p 136-137
“And what is it, bhikkhus, that the wise in the world agree upon as existing, of which I too say that it exists? Form that is impermanent, suffering, and subject to change: this the wise in the world agree upon as existing, and I too say that it exists."
-SN 22.94
Student, suppose there were a man born blind who could not see dark and light forms, who could not see blue, yellow, red, or carmine forms, who could not see what was even and uneven, who could not see the stars or the sun and moon. He might say thus: ‘There are no dark and light forms, and no one who sees dark and light forms; there are no blue, yellow, red, or carmine forms, and no one who sees blue, yellow, red, or carmine forms; there is nothing even and uneven, and no one who sees anything even and uneven; there are no stars and no sun and moon, and no one who sees stars and the sun and moon. I do not know these, I do not see these, therefore these do not exist.’ Speaking thus, student, would he be speaking rightly?”
“No, Master Gotama. There are dark and light forms, and those who see dark and light forms…there are the stars and the sun and moon, and those who see the stars and the sun and moon. Saying, ‘I do not know these, I do not see these, therefore these do not exist,’ he would not be speaking rightly.”
“So too, student, the brahmin Pokkharasāti is blind and visionless.
-MN 99
Here is Bhikkhu Bodhi summarizing the abhidhamma position on dhammas:
It is the dhammas alone that possess ultimate reality: determinate existence “from their own side” (sarupato) independent of the minds conceptual processing of the data. Such a conception of the nature of the real seems to be already implicit in the Sutta Pitaka, particularly in the Buddha’s disquisitions on the aggregates, sense bases, elements, dependent arising, etc.,…
…
Thus by examining the conventional realities with wisdom, we eventually arrive at the objective actualities that lie behind our conceptual constructs. It is these objective actualities – the dhammas, which maintain their intrinsic natures independent of the mind’s constructive functions…
…
…the commentaries consummate the dhamma theory by supplying the formal definition of dhammas as “things which bear their own intrinsic nature” (attano sabhavam dharenti ti dhamma).
…
…concretely produced matter…possess intrinsic natures and are thus suitable for contemplation and comprehension by insight.
…
Great seers who are free from craving declare that Nibbana is an
objective state which is deathless, absolutely endless, unconditioned,
and unsurpassed.
Thus as fourfold the Tathagatas reveal the ultimate realities—
consciousness, mental factors, matter, and Nibbana.
-Bhikkhu Bodhi, Acariya Anuruddha, A Comprehensive Manual of Abhidhamma, pages 3, 15, 26, 235, 260
And here is straight from the abhidhamma:
“All form is that which is…
void of idea,
neither feeling, nor perception, nor synthesis,
disconnected with thought,”
“form exists which is not due to karma having been wrought”
-Dhammasangani 2.2.3
And the Kathavatthu:
Points of Controversy
9.3 Of Matter as Subjective
Controverted Point: Whether matter should be termed subjective or objective.
Theravādin: If that is so, you must also affirm of matter or body, that it has the mental features of “adverting”, ideating, reflecting, co-ordinated application, attending, willing, anticipating, aiming—things which you would, on the contrary, deny of matter.
All, or any of them you can rightly affirm of mental properties, such as contact (mental reaction), feeling, perception, volition, cognition, faith, energy, mindfulness, concentration, understanding, lust, hate, illusion, conceit, erroneous opinion, doubt, mental inertia, distraction, immodesty, indiscretion—all of which you admit as subjective. But matter is not one of these, and therefore such things may not be affirmed of it.
You deny in the case of matter all those mental features—adverting, etc.—but claim for it the term “subjective”, which is really applicable to “contact”, sensation, etc. These, as you admit, do not lack those mental features named.
Uttarāpathaka: But is not matter correlated (as an object)? Of course you assent. Then as correlated it is surely right to apply the term “subjective” to matter, etc. since “object” is one of the twenty-four (causal) relations.
Thus, we can clearly see, Karunadasa confirms, as do the suttas, abhidhamma, etc. that Classical Theravada is a realist system.
Not only is external reality confirmed as indispensable, but both it and the eye must exist before eye consciousness is even possible.
Per Theravada, if external reality were non existent, as the Yogacara teach, then seeing, hearing, touching, smelling and tasting wouldn’t even be possible. This is, again, because the process of consciousness arising necessarily is preceded by external, existent physical reality.
The sense organ and external reality precede consciousness, and their contact is the precursor to consciousness arising. Thus they are clearly and undeniably mind independent.