If all your morals are relative you can sign on to do some reprehensible shit when misinformed about a situation because relative to what you know killing another person might be righteous. That is generally not the best way to handle anything. If your baseline isn’t an unshakable one based in human empathy idk what you really ever stand for
do you not think that people can't come to conclusions you would feel are terrible and still hold them as unshakable morals they derived from empathy? Do you think empathy is not subjective?
Your comment is that people can believe things are moral, that lead you to do horrible things, because relativistic morals make you susceptible to misinformation. You then say this isn't a good operating procedure because of this susceptibility, thus your morals can be twisted to justify horrible things, like killing people out of a sense of righteousness. Then you say that if your moral baseline isn't an unshakable belief, an axiom, based on empathy, you can't understand what the person believes.
The first part is true. However, how you present that last two sentences make it look like you are saying this is not good, and that having adamant morals, founded on empathy, is your understanding of a moral standing, and a better way of operating than relativistic models, which can be manipulated by bad input, and produce bad output.