For philosophy, nihilism is foremost the metaphysical nihilism, that is a nihilism in ontology and epistemology (there is no eternal ontological ground, in theistic terms, world doesn't have a creator, in any sense, and therefore has no unity as the world, this lack of unity, this unity is the concept of the world, therefore onlogical nihilism can claim that there is no world, just things).
I fail to see how metaphysical nihilism does not lead inevitably to moral nihilism. On what grounds do you establish morality. You can make rules codified into law reflecting the preferences of the majority but how can anything ever be right or wrong. At best you have the preferences of a majority or realistically the preferences of the ruling elite subject to change and personal expediency. What is the inherent significance of these rules? Nothing just transient strictures that carry a degree of risk if broken. If there is no world just things what does that say about humanity itself? Well we must simply be one more group of things with no real necessary value. If you can reach any other conclusion starting from metaphysical nihilism I am curious as to how.
You fail to see it, because the common metaphysics is a theological one, and for a theological metaphysics nihilism is just everything bad. You can establish morality on the grounds of knowledge and reason, and not on a shared belief. Majority consensus of believers is still just a different kind of theology, it measures beliefs not knowledge, but believing has nothing to do with truth, the number of people convinced is not an adequate measure of something being either true or just.
We have no real value just because value isn't real, but a property of knowledge. Like mathematics is not inherent in things, apples on tables don't have the inherent property of two-ness, this makes the predicate of quantity at the same time unreal, but true in an objective sense; the judgment has grounds in objectivity, yet isn't contained in it. This same distinction is pertinent to ethics, while things themselves aren't good or evil, facts serve as the basis of our knowledge of them as good or evil. Inherent significance is an oxymoron, there is only extrinsic meaning, yet this does not mean there is none, or that it is subjective in the sense that it would be arbitrary. So you have a thing X, a purpose Y, any only knowledge can tell you whether X is good for Y, the additional problem is to ground universal purposes, this is also possible with reason alone (but it requires a larger philosophical work, not a forum post).
This should not be confused with the simplistic claims that there is nothing, and we can't know anything as theists interpret it, but as its own metaphysical ground capable of producing rational ontology, epistemology and morals without succumbing to spiritualism. On this basis what we can say is that there is no intrinsic value, and therefore valuing is required as a finite process among other, susceptible to context and change, and because of that capable of progressing. To take values as fixed, therefore only blocks the potential progress of values and robs them of their rational basis.
Have you considered the possibility that the the end point of such a search the optimal rational ontology and morals may be ethical monotheism and if so the potential consequences of rejecting the optimum while searching for it. Ethical monotheism does not require a belief in spiritualism.
Some degree of spritiualism is necessary, although it becomes harder to spot and more abstract philosophical critiques are necessary to reveal it. Of course the rationalists in history were all theists, and monotheists (Spinoza has immanent monotheism as pantheism, Leibniz the transcendent monotheism of christianity), yet they were wrong, their systems contained assumptions no longer philosophically tenable.
There is a certain ironic elegance to a universe in which continued and sustained existence comes only to those who honor and respect its creator not via divine intervention but through inevitable cause and effect. Do we live in such a universe? It is entirely possible that we do.
Elegance is simplicity of function, it is inevitable as the mode of contingency, every star and stone and every mountain slope is a proof of impossibility of God's existence and a monument to the power of time.
Of course, the fact that the machinery of time holds all the other machinery of nature, is far greater evidence for God than of lack of a god.