Decouple the hard problem from determinism
Determinism/indeterminism is a different question than the hard problem. Physics is indeterministic. And both organisms, and our brain module, are both chaotic systems, which can therefore amplify small random inputs to the point of unpredictability. So a physicalist mind should be expected to be indeterministic. Whether a non-physical mind is or isn't indeterministic would depend on the details of how the non-physical ontologies work. But it is very possible a non-physical worldview would be deterministic, while physicalism would be indeterministic.
The things in our observed world are contingent so whether physicalism can explain consciousness is an empirical question
The radical contingency of our world means that we cannot evaluate physicalism vs. consciousness with intuition or rationalism. Physicalists deny there is an independent or causal Popperian world 2 (world of things that have time but no space, such as the way experiences and consciousness appear to us). As a general rule, in physicalist mind theories this is done with Identity claims between some non world 2 aspect of our world (neural states, functions) and consciousness. Critics of these theories note they fail the "identity of indiscernible" principle of identity, so should instead be treated as a "there is some fixed coupling between the non-world 2 feature X and the apparent world 2 feature Y".
The problem for physicalism is failing test cases
The hard problem is that the properties we have observed for consciousness have proven unable to be matched with a physicalist model. All physicalist identity theories have refuting test cases, primarily where consciousness is not present on occasions the model would predict it should be present. Some of these identity theories also predict no consciousness where consciousness is present. Also, as the contingent "just happens to be tied together" aspect of "Identity theories" rather than actual identity, means they logically map onto epiphenomenalism causally, and the causal refutation of epiphenomenalism therefore also applies to the "happen to be coupled" theories. Therefore Identity theory models fail the evolutionary test case which William James articulated against epiphenomenalism, and Karl Popper extended to identity theories.
Examples of falsified test cases
The earliest physicalists were neuro-reductionists Identity theorists. They assumed that conscious states were identical to a certain energized state of a specific neural structure. This identity came under attack through multiple realizability. Our own neural structures undergo continual rebuild, die-off of cells, and the energizing pattern moves around drastically and continually -- yet our thoughts and knowledge stay pretty stable through all this tumult. Additionally, we can communicate thoughts to others, who have very different neural structures, and other creatures can also do what clearly is equivalent thinking (say counting, or an effort to deceive showing theory of mind) despite even more radically different neurology. Within our own thinking, the "logic state" has to be maintained as a homeostasis by a brain, and therefore the logic condition becomes a causal driver of changes in the neural state. Additionally, while we built our digital computes based on our introspection of how we consciously reason, there is no digital computer architecture anywhere in our brains. Reasoning explicitly cannot reduce to neurology, based on what we discovered about how our neurology is wired. The criticality of logic sates and functions to how we do homeostasis, how we communicate, and why we think other creatures are conscious, and the ability to describe reasoning functionally, are why most physicalists have switched from neural identity theory to functional identity theory. If one maps this to Popper's 3 worlds, this is a world 3 coupling to world 2, as opposed to a world 1 coupling.
Paul Churchland, one of the remaining neuro-reductionists, asserted that conscious just IS our recursive neural nets processing. However, ALL of our brain processing is the operation of recursive neural nets, and 99.99% of that processing is not conscious. Churchland's model is easily falsified by the simplest of observations.
Functional identity theory has a very similar problem to Churchland. 99.99% of the functions our brains perform are unconscious. Plus it has another problem, in that all sorts of other things do functions, but do not appear to be conscious.
AI theorists initially addressed why their computers were not conscious despite doing functions, by postulating that some additional feature, such as through put rate, was necessary for the coupling between functions and consciousness to emerge (an emergent throughout could also explain why leaves waving in the wind, and rocks breaking apart were also not conscious). But after many orders of magnitude increase in our computer speed, with no consciousness appearing, this idea has been abandoned as refuted.
Alternate theories have been proposed. One such is that only functions that self-reference -- higher order processing -- could be conscious. But sit on a mislaid pin, and one is VERY aware of the pain and leap back to one's feet, well before one starts doing any higher order processing about it! Alternatively, Global Workspace Theory holds that the shared data between processing modules is what we are conscious of. But GWT would hold us to be conscious of driving, and NOT of daydreams, but all of us who drive have at times gotten lost in daydreams WHILE driving! Integrated Information Theory holds that only functions which run on a high Phi network are conscious -- but again ALL of our brain's functions run on the same high Phi network, but 99.99% of them are not conscious.
Many of the philosophic thought problems that have driven philosophy of mind in the last several decades have focused on qualia, as qualia are non-functional in functionalism, and are therefore a challenge to functionalism. Mary the Color Scientist gains knowledge when she finally has a color experience. Whether one's experiential spectrum is inverted or not is a "fact of the matter" but cannot be established functionally or neurologically. The Chinese room can do the function of communicating in Chinese, but there is no qualia experience of knowledge of Chinese in it. These all are test cases against functionalism.
These problems for physicalism have led to the rise of "Delusionists", who hold that physics tells us physicalism must be true, so if consciousness data refutes this, then consciousness data must itself be in error -- a delusion. See Susan Blackmore's A Very Short Introduction to Consciousness for a very clear argument for throwing out consciousness data on these grounds. This is, of course, to reject science, as in science data is king, and theories (such as physicalism, dualism etc) are what one throws out when data contradicts them, not the other way around.
Where is the philosophic community on physicalism?
Among philosophers of mind, there are advocates of every one of these physicalist views, who argue that THEIR version of their preferred model stands up to these refuting test cases. As a general rule, however, each of these claimants has not been able to convince even their physicalist rivals. So while physicalism remains popular, there is a wide consensus within philosophy that every specific attempt to address the hard problem of consciousness has failed, even though most physicalists may think THEIR approach works.
Note that all theories are capable of being "vagueified" to the point when they are not testable/refutable. Vaguification is also done by many physicalists who admit that specific physicalist theories are unable to address the failing test cases. Vaguification is also often coupled with the "someday somebody may find an answer" embrace of the Duhem-Quine thesis. Duhem-Quine IS True -- every theory is infinitely modifiable, hence someday someone may find a way to make physicalism compatible with consciousness. But empiricists don't resort to Duhem-Quine, and instead use the models that actually fit the data. Rejecting empiricism based on the Duhem-Quine "maybe someday" is always possible. But it is to reject science, because one can resort to Duhem-Quine to reject every science theory as well.
Vaguification, and invoking Duhem-Quine, can be appropriate if there are no good alternatives to an otherwise useful theory. Physicalism IS useful -- that was Papineau's point in his excellent paper "The Rise of Physicalism". But the limits of reductionism, the reality of emergence, the adoption of scientific pluralism, and the widespread rejection of scientism are all subsequent to "The Rise of Physicalism", and suggest that physicalism is a useful heuristic, but not a global Truth -- decreasing the strength of the argument for ignoring a failing test case.
This is why alternative ontologies have increasingly been considered as live options in philosophy:
Fregean triplism.
Scientific pluralism.
Popper's emergent dualism.
Eccles substance dualism.
Property dualism.
Russellian monism.
Various pan-psychisms.
Mathematical idealism as with Tegmark and Hoffman.
Mental idealism as in the Perennial Philosophy.
The spectrum of live options to physicalism has opened dramatically in the last several decades among philosophers.