For one, you say "all matter is composed of neutrons, protons, and electrons" but what about subatomic particles?

Just some thoughts on this, about the levels of complications (not what qualifies you as literate). When we learn, we learn in stages and often in simplifications. You don't start by learning about gravity as spacetime curvature, you start in high school with algebra-based mechanics using forces, which is an approximation of general relativity in some low-mass, low-speed regime. This allows you to understand a lot of physics without being able to do the complicated math of the more complicated physics. And I think that's okay for some threshold in literacy, for example.

Understanding neutrons, protons, and electrons, which are subatomic particles (I assume you meant what some of those are made of, like quarks), allows you to understand how nuclear physics works at a level where you don't need to understand the entire Standard Model of Particle Physics, which becomes incredibly more complicated in math. If you understand that there is a more complicated model and a little bit about it without getting into all of the details, then you've learned a certain level of science, typically high school level, rather than graduate level, which is fine if you don't really need to study particle physics.

the answer is that one should have a cursory knowledge of all accepted scientific concepts

Perhaps, but what does "all" mean? How much astronomy does one need to know to be considered scientific literate? The Big Bang? Probably. How stars work? In my opinion more so even though I think less people know something about that than the Big Bang. What about something about pulsars? It's an entirely separate field of astronomy but I wouldn't consider someone scientifically illiterate without knowing it. I understand a little bit of how biological evolution works but there are probably equivalently "small" fields in biology that I've never even heard of. Hopefully that doesn't make me scientifically illiterate!