Nietzsche is surely right that people's morality changes all the time. Both individual and in whole societies. And certainly right that they flow from some unconsciousness places inside of us. [The irrational unconscious of Schopenhauer.]
But that does not show that there is no objective morality. Rather that it is hard to get to.
[He was attacking Hegel on that score. Hegel thinks that people keep on progressing towards the Absolute Idea. Well, yes and no. There is objective morality, but we do not progress towards it at all and there is no reason to think that we now have it or will ever have it.
But as Michael Huemer points out that just like in math you can start with very simple assumptions and build a lot on that, so in Ethics it might be possible to start with a simple axiom and build on that.
In math that works by you have the idea of a number and add to that the idea of a vector and then the idea that things have shapes. These are not hard assumptions. Then you come up with Vector Calculus and Algebraic Topology. So in ethics you might start with a simple rule: one should not torture millions of people for the fun of it.
In fact we do find in the Gemara that the laws of the Torah have simple reasons. The Gemara however never tells us what they are. But later you find starting from Saadia Gaon and Ibn Pakuda that the reasons for the laws were made more explicit. --[Not to do idolatry or believe in idols, rather to believe and trust only in the First Cause. Peace of the state.]
[The hidden assumptions are in the modern world, not so hidden. The problem is not that they are hidden but rather that they are unexamined. The advantage of philosophy is that one learns to examine his or her assumptions about right and wrong. Feminists for example start with the assumption that they have been abused. That is perhaps sometimes true, but it is an unproven rule. Perhaps some girls have had good parents? I know for example that my mother had good parents.]
This mentality gives rise to the "Me Too" movement. And comes from a phenomenon seen by Nixon: that Americans believe in the news media more than they believe in their own eyes. Thus people will believe things that they are supposed to believe, - even when their own experience tells them that those beliefs are untrue.
