Moral realism

I want to be precise.
A sentence that expresses moral content, such as "murder is immoral," can be said to be true or false.
But a sentence that expresses a norm, such as "murder is forbidden," is not true or false because it depends on which system you obey, so there is only binding and non-binding. Right? (But someone who believes that "murder is immoral" will necessarily accept that "murder is forbidden" is binding.)

And something else. Is there a connection between moral anti-realism and postmodernism? Each one has its own narrative - there is no existing morality, everything is a social and personal construction.

I don't see a difference between these two sentences. “Thou shalt not murder” This is a commandment and there is nothing to discuss about truth or falsehood.

You are not talking about anti-realism but about anti-objectivism. It is possible to link this, although in relation to morality many think so even before postmodernism.

So I didn't understand the difference between realism/objectivism on the one hand, and anti-realism/relativity on the other.
If the saw is real, then it is objective (and vice versa), and if it does not exist in reality (anti-realism) then it is subjective (relative) and vice versa.

I explained the difference above. If it is realistic then it is objective, but not the other way around.

According to moral realism, how does the fact that the object "murder" has an "evil" characteristic/attribute normatively obligate me not to commit murder? That's the naturalistic fallacy, isn't it?

I explained this. Ethical facts are not related to a naturalistic fallacy. Norms can be derived from them. From the fact that it is forbidden to murder, it can be deduced that it is not permissible to murder. Beyond that, there is the requirement of God Almighty to obey these facts.

Sorry for the dig but:
1. Above you wrote "I explained the difference above. If it is realistic then it is objective, but not vice versa." But you didn't explain, you just stated that there is a difference between the two, without explaining what the difference is. So I didn't understand what the difference is between them
2. Here you also wrote "I explained it" but I don't know where you explained it. You just stated that norms can be derived from ethical facts. But the question is, why??

1. In the first post here I explained this. Here is the quote:
Moral objectivism is the view that morality is objective and not relative. Moral realism is the view that morality exists in some sense.
From this you can also understand that the real entails the objective but not the other way around.
2. Why not? This is exactly the difference between ethical facts and ordinary facts. The naturalistic fallacy talks about ordinary facts. But an ethical fact is that it is forbidden to murder, its content says that there is a prohibition, that is, there is a norm. Therefore, here the norm can be derived from the fact.

Regarding objective-subjective, is the color of the table in front of me an objective or subjective fact (=everyone and how they see the table, some will see it black and some will see it white)?

And regarding the issue of this thread, you as a realist and moral objectivist, how do you justify the fact that there are so many disputes in morality? Today's morality is not yesterday's morality and not tomorrow's morality.
If everything is objective, how are we supposed to decide the difficult questions of ethics. For example, is polygamy moral? Is contraception moral?

This is the philosophers' chestnut. We have no way of checking it. Furthermore, what I see when I look at the table may be what you call hearing Beethoven's Ninth Symphony or a type of consciousness that is completely unfamiliar to you. One thing is clear, there is no necessity for everyone to see the same thing. If a person connects the waves of the wavelength of red to the center of yellow in the brain, he will see them as yellow. There is nothing essential here.

Regarding morality, first of all, there are not so many disputes. They are on the margins. The great majority of things are agreed upon, and this is itself an indication of objectivism. Beyond that, there is also development over time in scientific knowledge, and this does not mean that science is subjective.