This is already a thing in our world
I know people from a rural part of Honduras where it is common to raise insects as food. The area they are from is still pre-industrial with most people living on family farms, working the land with hand tools, and making most of thier own stuff from local resources. Honduras is also a tropical country... so the only thing that is really different from your setting is that Honduras also has other kinds of edible fauna, but that hardly impacts the outcome of the question.
Also, neurotoxins will not keep people from eating the other animals too
Eel blood is full of a deadly neurotoxin that is destroyed by cooking. Puffer fish and various snakes have very deadly venoms, but are still eaten when carefully prepared such that the venom does not contaminate the meat. Cassava is rich in cyanide which is processed by soaking and fermenting it for a week before it can be processed into an edible flour. Greenland shark meat has toxic levels of urea which requires the meat to be cured and fermented for 4-5 months before it is edible. These are all forms of meat people figured out how to eat safely using pre-industrial technology.
Insects and other arthropods also fall into the realm of "less than safe" kinds of food because of the high prevalence of parasites, but various preparation methods like cooking to very high internal temperatures and boiling with parasite killing spices have also made these animals safe for consumption using methods that predate industrialization.