You can in theory use any semiconductor junction to build nonlinear behaviour, and that's enough to implement logic, and that's enough to implement a CPU.
Of course, since you might want to still be able to power them, a composition with a reliable and still low band gap is necessary.
You'll find it's no coincidence that Si is the usual semiconductor, and that the available adjacent groups in the periodic systems limit your choice of elements to use as dopant.
Realisitically, if any other simple anorganic materials would be easier to handle or cheaper to use to produce working semiconductors, even bad ones, then they would already be in use. You'll find, for example, that Copper oxide- and Selenium-based diodes used to be produced, but they were so bad that the harder-to-make silicon diodes have completely replaced them. Same for Germanium, and a few other materials. You can investigate these obsolete technologies, but you'll quickly find out that people tend to care more about materials not being toxic than they did 50 years ago...
A field that might still be yielding new materials that can be used in semiconductor junctions are organic semiconductors, like you already find them in organic light-emitting diodes. That's not saying they are abundant, or can be processed "with relatively few resources", but really, what technical material is?
In the end, I think you should be looking into the homebrew semiconductor community. There's people building ICs in their garages! They still have to use rather nasty chemicals, and have to buy raw wafer materials, mostly, but the truth is that a monocrystal of an any significant size is hard to produce without industrial style processes, and that applies to semiconductors as much as to e.g. artificial sapphire or diamonds for technical applications.
All in all, I think as broad as your question is, you underestimate the complexity of all this. Building a CPU will take at least hundreds to thousands of transistors, and you need them to be reliable, and you want them to be reasonably effective at what they do, lest you get in real heat and power supply trouble.
By the way, aside from maybe the iron(II) oxide, I don't think your substances could be described as non-toxic at all.