And what exactly is the implication of there being no valid and binding morality?
Also, I’d be happy if you could point me to where you addressed the irrelevance of moral relativism, and also your view as to why it does not exist.
Thank you very much!

Even if there is no implication at all. The question is what you believe. All of this is explained in the notebook. That is the whole point of the fourth notebook.
As for the relativity of moral values, I indeed didn’t find it there. I’ve now added a section dealing with it. Here it is:
A central objection to the argument from morality is the claim that moral values are relative. If God created morality, how can it be that every society and every person are committed to a different value system? After all, there is one correct system, the one God created and demands of us.
First, it is important to point out a flaw in this objection. The fact that there are different moral values in different societies is a fact. That does not mean that normatively they are all right. It may be that there is one correct moral system that God demands of everyone, but some people and societies do not perceive it correctly, simply because they are mistaken. After all, differing views are also possible on factual matters (for example, whether a socialist economy leads to higher GDP than a capitalist economy, whether political moderation will bring peace or war, and so on). Does that necessarily mean that there is no truth here? Of course not. There may be a truth (in factual contexts there probably is), except that one of the disputants is right and the other is wrong. The fact that there are two opinions does not necessarily mean that there are two truths, that is, that truth itself is subjective. We have already seen the naturalistic fallacy, which holds that one cannot derive value conclusions from facts alone. The fact that different societies hold different moral systems is only a fact, and as such no normative conclusions should be drawn from it (that all these systems are correct, or that there really are several valid systems).
But beyond that, even the factual assumption itself—that moral values are relative—is not accurate. After all, regarding most moral values we all agree. Who disputes that it is forbidden to steal, murder, and harm others? Or that it is important to help others, make them feel good, and so on? All of these are agreed values. It is enough for us that there are agreed values in order to ground the argument from morality. After all, these are absolute values, and God demands them of us and gives them validity, even if all the other values are disputed and subjective. There are, of course, arguments even regarding these central values, but they are fairly marginal. It seems to me that almost all of them deal not with the values themselves but with the question of their application (is it permissible to murder fetuses, Jews, Gypsies, the disabled? Is it permissible to steal from a thief? Is it permissible to lie in order to save oneself from theft, or perhaps just to flatter?). But these disputes show that the basic prohibitions themselves (murder, lying, theft) are agreed upon.
Beyond that, even if we accept the possibility of deriving normative conclusions from facts (that morality differs across societies), the argument about the relativity of moral values is challenged from another angle as well. Take for example an encounter between a European society with Western (Judeo-Christian) morality and an African society of cannibals and pagan idol worshipers. Usually, what happens is that the African society adopts Western values. I have never heard of a Western society whose members began to eat human flesh or gave up democracy after such an encounter. By contrast, I certainly have heard of societies that adopted democracy and Western values and beliefs generally. That is, even if we accept the fact that there is a multiplicity of value systems, it is still hard to ignore that this process has a direction; that is, change tends to happen in fairly clear and defined directions. Does that not point to an advantage of the modern direction? Even if there are societies that advocate other values, in encounters they usually move in the modern direction. Therefore, even if we want to draw normative conclusions from the facts, we must also take into account the superiority (at least on the factual plane) of Western values. Of course, those who hold postmodern views will explain that these are schemes and exercises of power by means of which the West takes over the Orient. That is, of course, nonsense. There is an exercise of power, but the process of value change points to something much deeper. There is an expression here of progress, as human societies repeatedly discover more correct values and move toward them (forgive the blunt modernism).
And beyond all that, even if there really is relativity in moral values, that does not touch the argument from morality. Even if there are two societies or two people who believe in different moral values, each of them still has to account to himself for the values in which he himself believes. How can there be such a thing as a norm or a value in a materialist world or in a world without God? Each person as such is supposed to arrive at the conclusion that there is a God on the basis of his own values, even if those values are completely different from those of the other person. The other person too will arrive at that same conclusion, and by the same route, of course. Our argument does not depend on the universality and uniformity of moral values.

Interesting. My questions:
A. From several places in the text, it sounds as though you really think one can and should infer from the morality found in the world—that is, that you do not really accept the claim of the naturalistic fallacy. I may be mistaken, of course, but that is definitely the impression: that it seems reasonable to you to infer morality from what exists.
B. As for the process of moral change, one can of course suggest an alternative thesis: the morality that takes over is that of the stronger society. In principle one could also try to examine this in historical cases, but I do not have enough knowledge to provide an example.

A. I do not recall such a place. Of course I can lend support to a moral statement from the fact that this is how people in the (“enlightened”) world tend to think. Determining the content of morality can be aided by what people think (a sentence like: a reasonable person feels that this or that is the right thing to do in such a situation). But deriving moral relativism from factual plurality is a fallacy.
B. I mentioned that thesis. My feeling is that this is not the case. It is hard for me to accept that if the Africans had much greater power than Europe, then following such an encounter we would begin eating human flesh and abolish democracy (of our own free will—that is, stop believing in it).