What determines whether or not you "should" do something?
My thoughts are that "should requires an axiom". You could say "you shouldn't kill people... if you don't want people to suffer". Or "you should kill people... if you want to go to jail".
In practice, I think people have similar ideas about how outcomes make them feel. Outcome X feels just. Outcome Y feels unjust etc.
When people use the word "should", I think they're implicitly saying "should... in order to achieve the outcomes that me/society feel are just".
This is basically the issue of whether categorical imperatives are a coherent concept. I have the same feeling as you: that they are not, and that I don't even understand what it would mean for them to be. I'm continually baffled by the fact that so many human minds are apparently able to believe that categorical imperatives are a thing. This strikes me as a difficult problem somewhere at the intersection between philosophy, linguistics, and cognitive psychology.
I was stunned to read the accounts quoted below. They're claiming that the notion of morality - in the sense of there being a special category of things that you should or should not do for the sake of the things themselves being inherently right or wrong - might not only be a recent invention, but also an incoherent one. Even when I had read debates about e.g. moral realism, I had always understood even the moral irrealists as acknowledging that there are genuine moral attitudes that are fundamentally ingrained in people. But I hadn't ran into a position claiming that it was actually possible for whole cultures to simply not have a concept of morality in the first place.
I'm amazed that I haven't heard these claims discussed more. If they're accurate, then they seem to me to provide a strong argument for both deontology and consequentialism - at least as they're usually understood here - to be not even wrong. Just rationalizations of concepts that got their origin from Judeo-Christian laws and which people held onto because they didn't know of any other way of thinking.