The Analytic and Continental traditions in western philosophy are not entirely distinct, nor are either monolithic; while the analytic may stress clarity and structure and the continental with ways of life and foundations, this classification is only an approximation, and one of many that approximates a division is stronger when mapping philosophical genotypes than expressed traits. The analytics have traditionally staked a stronger claim to science; incorrectly, I think, although the relationship between science-as-natural-philosophy and other areas of philosophy have a number of conceptions depending on the subschool of philosophy. I hold that strict materialism and empiricism are compatible with subjectivity and the broad continental programme, and lay out my preferred frameworks in each (without argument, as I think these positions sit on axioms or things near them that are both difficult to unseat and are competing with other theories that are likewise difficult to unseat; except in rare cases one is left making aesthetic arguments between them as each is reasonably consistent).
I believe a good metaphysics begins with either the questions of solipsism or potentially below that at the question Descartes was addressing, and cannot prove its way from that point but must hedge slightly and make pragmatic steps, and to reach a reasonable perspective it must in fact hedge and be pragmatic many times. Cogito Ergo Sum is a simple nonsequitor; once we understand thought as embodied in the mind and revisit it with the understandings given by modern science, there is no requirement that a pattern of brain-states that represent a thought must be instantiated anywhere; the subjective cannot more than pragmatically justify the objective, and the philosopher who would be a logician (a generally misguided figure) cannot in fact prove their existence any more than our consideration of their thoughts necessarily instantiates any more of them. Likewise, there are no means we can use to prove the universe exists in the logician's sense. We accept the reality of the universe and a great many other things through these pragmatic steps long before we find the upwards stairs of philosophy, and ideally swiftly outgrow misunderstandings about logic by trying to apply them to these foundations.
We acquire empiricism pragmatically; it works, and we come to appreciate the human faults it plays against through experience in the world. Likewise, we see that a culture of empiricism and criticism is capable of correcting more faults than empiricism in one individual alone, giving us the concept that natural philosophy must be embedded in academic culture (in modern times, peer review and tiers of journals and funding-chasing and tenure), while in political philosophy everything from jesters to pluralism to bureaucracy and independent media provide the same balances against individual faults; the notion that ideas should be weighed on merits and come from careful consideration rather than power politics, and that these ideas should win or lose based on their performance and that there should be consequences (from loss of credibility to personal loss) for their failure, these peel us back from instinct and herd mentality and preserve us from various kinds of corruption.
On delineating natural philosophy from value philosophy (or in common parlance, science and philosophy), we isolate natural philosophy as a whole as concerned with facts (meaning questions about the state and rules of the universe), with each science having its own standards of inquiry and its own community and its own specific fields of interest for claims. Claims outside of natural philosophy either become their own fields in a similar fashion (such as maths or history) or remain partially or wholly undifferentiated in philosophy. The key feature of each differentiation is when it steps from a high level of divergence to relative or high convergence, and when it can defend these claims as being caused by more than specificity of school (meaning that creation of a tradition of strict rules within a broadly philosophic topic is not intrinsically enough to mark that tradition as a science; the structure must be justifiable, and occasionally there may be intellectual struggles over the validity of a field-as-it-is or a fields-intrinsic-merit).
In philosophy of science, I am an Instrumentalist, and claim that Instrumentalism is the most intellectually coherent form of Empiricism; there is no way to more-than-pragmatically verify congruence of any theory to reality itself, and given the hedges we already must have made to reach the point of doing natural philosophy, instrumentalism accepts the inherited hedges in a way that other philosophies of science do not; likewise, we could not eliminate the idea that our nature is a simulated world, but we can mark the question as irrelevant by conceiving the task of science as being an exploration of apparent reality; whether simulated or not, the task remains the same, and only should we both somehow discover the falseness of reality and open new fields of natural philosophy to study nonapparent reality will that task significantly change.
I pragmatically accept, having studied science in general and brains specifically, the idea of the mind as an abstraction of the function of the brain, entirely caused and understandable-in-principle in terms of the physics of its components. From this perspective, the claim of free will as classically conceived is marked false (although it was already difficult to coherently state its principles). Our lack of ability to predict the future state of the universe is limited by a lack of information about our own brain and the rest of the universe as well as a lack of enough computing ability to bring to bear on the task (presuming that there are not probabilistic factors intrinsic to the nature of things rather than as a fudge for lack of information, which I don't entirely commit to).
With this statement about the nature of things as I understand it, there remains quite a lot open for philosophy; the basic apparent fact of reasonable or full determinism (that probabilistic hedge distinguishing them) doesn't eliminate questions of should, or questions of the meaning we can or should or might be persuaded to assign to our lives. We may empirically discover ourselves to be creatures that live lives of stories, or understand how and when and why we love, but mapping those sides of human nature doesn't require or even suggest to us changes in how we should live; we remain capable of setting our ends in any of the ways we're exposed to or think up, and capable of writing stories as limited by our creativity, or at least we are locked into the delusion that we can. Working with that, we still subjectively have many degrees of apparent freedom, and philosophy and art and various other fields remain as open to us with that realisation, provided they don't make truth claims, as they did before that realisation. Continental and Analytical philosophy, with some sensible limits, have most of the usual questions and areas of inquiry left to them. There are some interactions between any natural philosophy-compliant value/life philosophy and natural philosophy that the value/life philosophy would need to deal with (inconvenient facts and all), but with appropriate humility and thoughtfulness on those topics, this can be managed.
Likewise, when we are asked a "why" for a question about human behaviour, we should differentiate "why do humans X" from "why should I X" (or "should I X") as questions; we may decide to value the factors we see in an objective analysis of a behaviour situated in a social dynamic, or we may decide to create independent reasons or reject-as-should those factors (possibly creating a new preference for a dynamic, or preferring a shift to the dynamic present in some other society that we've studied). An absence of a should is only possible if we're studying a hypothetical or no-longer existing society, and even then the thought experiment beckons to the thinker.
As an example of an inconvenent fact that might come up, if we have a commitment to treating people of certain groups the same that comes from our political philosophy and sense of social justice, any scientific inquiry that showed concrete rule-or-statistical differences between the populations we're committed to treating equally would be inconvenient, and an immature political philosophy would either prefer never to ask the question (bad) or insist that the science must reach a certain conclusion (worse). A mature political philosophy would see it as a legitimate scientific question and be able to deal with keeping whatever commitments it keeps to treating the populations equally while fully and openly acknowledging the results of scientific inquiry as much as were it to turn out conveniently. (Note that my commitment to this is one of the several things that inspires my stance against political correctness; PC builds bad mental habits that could hamper science; all scientific questions must be askable and their results acknowledgable even were that acknowledgement feel oppressive or insulting, and science necessarily tramples religious and cultural gardens in ways that some will feel oppressive).
None of this can support the two-majisteria-claims of religion-science compatibilists, as religions make truth claims, and those are subject to examination by natural philosophy as a whole, specific sciences, or history. This is not a two-spheres framework anyhow, as science is a subfield of philosophy rather than a separate field, with religions being broad-philosophy done badly.