Sentience is, on my analysis, the central criterion for an entity's having moral standing or moral status (meaning its well-being must be taken into consideration if it may be benefitted or harmed by a decision, action, policy, law, etc.) both within Buddhist ethics and within utilitarianism (the ethical theory that holds that the right thing to do is always whatever will produce the greatest overall good for the greatest number of individuals affected by the decision, where 'good' is usually translated to mean something like well-being or benefit, and often simply as any pleasant consequence). I'm not arguing that there are no other, equally good reasons to draw a line that differentiates between beings that have or lack moral standing, but simply not addressing them here. My point in noting that sentience functions in this way is simply to highlight the moral importance of sentience, as an introduction to the question, which classes of beings, if any, are not sentient? It is assumed generally that animals are sentient (able to sense, feel, perceive), though it is also generally assumed that plants are not sentient. Sentience is the ability to sense, feel, or experience, and so it seems intuitive that anything that is assumed to be sentient is experiencing some minimal form of consciousness, although not necessarily complex consciousness, such as thought. The question of 'panpsychism' is whether not only non-animal plants are sentient, but whether all non-animals are, and that includes inanimate, lifeless matter: Is it possible that everything is conscious?
Since the question is whether lifeless matter can be sentient, it is misleading to ask whether 'non-sentient matter' can be sentient, for that way of wording the issue presupposes that it cannot be sentient, by definition ("non-sentient matter"). Panpsychism is the view that the answer is yes: all matter and energy can be sentient, and is, in at least some very primitive sense. I prefer to call panpsychism 'physico-sentience', to restrict the claim of sentience to everything that may be acknowledged by physics, namely, all forms of matter and energy, so as to exclude non-concrete abstract objects such as numbers, universals (concept categories, like rectangular, seven, etc.), and conceptual relationships (such as 'is greater than'), etc., but I'll flip back and forth between 'physics-sentience' and 'panpsychic' simply to remain within the easy access norms of the larger linguistic community.
Arthur Reber makes a compelling case for non-animal organisms and possibly any organic matter being sentient, in "Caterpillars, consciousness and the origins of mind", and in his forthcoming book, The First Minds: Conversations with a Caterpillar and some Sentient Cells (Oxford, 2018), very similar to the broader panpsychist claim that non-animal matter altogether can be sentient, because there is good empirical evidence in support of what I'll call 'biosentience', but he argues against going that far (to all matter and energy) because doing so exceeds the evidence and threatens to become an evidence transcending hypothesis, among other reasons. After all, we know animals are conscious, we doubt plants are, and we have no evidence that inanimate matter is, so Reber demarcates the domains of conscious and not somewhere on this side of the organic line. But comparing biosentience and what I'll call 'physiosentience', so to speak, helps clarify the issues.
The main argument for physico-sentience is conceptual, explanatory, philosophical, not empirical, so it might survive Arthur's criticisms: complexity alone does not seem intuitively capable of explaining how molecules can generate something that it is like to be a complex collection of them, no matter how complex, even if that can explain how systems of them can become self-replicating or locomotive, as these latter properties can be completely explained by reference to the details of the material configurations. Thus, one way to explain consciousness is to suppose that all conditioned phenomena, as the Buddhists might put it, or all matter and energy, as Western philosophers and scientists might put it, experiences at least some rudimentary form of sentience. If that is true, that would explain how complex minds could arise from simple sentient particles, in the same way that mountain ranges can be explained by plate tectonics, which can be explained by ... molecules in motion.
One possible counter to restricting sentience to bio-sentience might be to challenge bio-sentience as too broad. Plants do not seem sentient, so maybe instead of bio-sentience the claim should be restricted to animals, say, 'anima-sentience'. But complex security systems are able to detect and respond to perceived threats, and they do not seem sentient either, so perhaps animals are not really sentient, but just function as if they are. The standard reaction to this line of thought is to refer to one's own demonstrable sentience: I'm experiencing sentience right now. Some philosophers, however, argue that even our own sentience is an illusion, a function of a complex set of evolutionarily valuable representational systems that give the appearance of sentience because that illusion is user-friendly, efficient, and so on. That would be the opposite of physico-sentience, what may be called 'null-sentience'. Null-sentience is hypothetically possible, but, like physics-sentience, it far exceeds the empirical evidence.
Interestingly, as I have argued before, Buddhists and utilitarians might be missing an important, more fine-grained distinction between cognitive sentience and hedonic sentience. Though they are being referred to as species of the same genus, they may not actually share a genus, more than merely nominally, or as a function of inadequate taxonomy. Let me explain. According to DeGrazia, in Animal Rights: A Very Short Introduction (Oxford UP), animal research suggests that insects might have the plumbing, so to speak, for pain, but not the hydraulics, so to speak, for whereas other animals will avoid using a damaged limb, for example, insects will not. These are clearly beings that have cognitive sentience, that is, they can sense or perceive aspects of their environments and obviously respond with appropriate motor control over their limbs, etc., but they may lack hedonic sentience, that is, there may be nothing it is like to be them, they may lack feelings altogether in the sense of pleasure and pain. If that is correct, they may be like those security systems I mentioned above, which involve cameras, pattern recognition software, motion sensors, etc. and the motor-control ability to lock down the museum. If that is right, then either cognitive sentience is not really a species of sentience, other than in word, or if we insist on considering it a species of sentience, then cognitive but non-hedonic beings may be sentient but arguably lack moral status and moral standing, just as security systems do, in which case Buddhism and utilitarianism would need to revise their previously too-broad criterion of sentience to a more narrow criterion of hedonic sentience or just hedonic beings.
From a Buddhist perspective, however, it is arguable that, if those insects have cognitive (perceptual) states (they do have eyes, they orient well, etc.), and if those cognitive states count as mental states (momentary states of mind, however simple), then even though their metaphorical plumbing for pain might lack the metaphorical hydraulics required for pain, there is something it is like for those insects to have those mental states, to perceive, in which case they are appropriately thought of as capable at least of mental suffering, and thus they count as sentient beings, sentience is the proper genus containing both cognitive and hedonic states as species, and it remains correct for Buddhists to treat sentience as the criterion for moral standing or status.
I hope you can see where this is going. If panpsychism is correct, then Buddhists need to become more pacifistic than Jain monks, who sweep the streets in front of them with gentle feather brooms so as to avoid harming microscopic insects they might step on, since everything made of matter and/or energy would have cognitive states, thus mental states, thus be capable of suffering. Utilitarians would probably not have the same problem, as they employ a cost-benefits analysis, so no matter what they did there would always be a cost in a panpsychic world, and that would simply have to be taken into their equations, but the evidence for the degree of suffering experienced by the sidewalk by their walking down the street would probably correctly be evaluated as so minimal as not to interfere with their ordinary activities or equations.
Insects might not have minds, however, just like security systems apparently don't. But they might. I like focusing on them because they raise doubts against the bio-sentience theory, simply by demonstrating the possibility that evolution has eliminated the less fit designs of ancestor insects, and has produced beings that are almost as complex as we are, and comparatively as intelligent (think of the 'dance' that honey bees perform to transmit information to other worker bees about the location of flowers relative to the hive), but quite reasonably without minds. Yes, we seem to have both cognitive sentience and hedonic sentience, but if wasps might lack both, maybe we do as well, on the one hand, but maybe everything possesses some rudimentary form of sentience, on the other hand. By looking at bees, bio-sentience theory, the strongest argument against panpsychism, seems uncertain, as bees might be mindless analogous of security systems, and their complex status as cognitive/locomotive living beings is no guarantee that they are sentient at all, in which case biology might just coincidentally be correlated with non-primitive forms of sentience we can recognize in some cases but not others, but primitive sentience might be intrinsic to all matter and energy. After all, all matter and energy is causally interactive: able to be causally influenced, and able to exert causal influences.
This is a form of sensitivity: sensitivity to interaction, which changes the state of the thing causally impacted. In early Buddhism and especially later Buddhism, being able to enter into causal relationships is the basic criterion for anything (within the realm of conditioned phenomena, or matter and energy, as opposed to nirvana, which is thought of as unconditioned) to be considered real or really existent, and that 'causal-ontological' criterion, as I've termed it, has been applied to argue against the real existence of abstract objects like universals (e.g., the property of squareness, as opposed to an object that is square-shaped, numbers, etc.) as well as the Vedic concept of the immaterial, changeless soul or atman: if it cannot change, it cannot enter into causal relationships. Similar arguments have been pressed against Cartesian immaterial minds: how can they interact with anything physical, like that soul's body as opposed to someone else's, if nothing causally links them to that body? The point of all this talk about causality is that the causal-ontological criterion might not only apply to the existence of real things, but to the possibility for anything to be sentient, sensitive, able to be altered, and thus possibly to panpsychism. One puzzling question for Buddhists, on this line of thought, is whether anyone can ever really experience the unconditioned state of nirvana, if the causal-ontological criterion holds not only for existence, but for sentience? I'll leave that question open for now, but I address it in my forthcoming book on Buddhism, meditation, and free will (Routledge, 2018), the title of which is still undecided, but of course I'll post links to the book once it is in print.