This logic would likely extend to all food sources.
Animals are a risk to the community, as they may mutate and attack their peers as well as the humans breeding them. And that’s if you can even keep them alive from the constant pressure of outside predators. EDIT: This reminds me of the “Feed” by Mira Grant – I believe horses over a certain size were outlawed to prevent potential spread of the virus. Similar also to the I Am Legend film, where keeping his dog seems great and all, but is ultimately a potential threat to his own life.
Grown food would likely also be affected by some aspect of the Cataclysm, whether that’s radiation, the blob, fungus, or any number of unknown factors. We don’t really have mutated crops in-game, but I don’t see any reason to think it wouldn’t happen.
The only scenario I see for humanity’s survival is to sequester themselves deep underground and, ideally, find a way to thrive living in the dirt. Even that’s not really do-able, as we can see in Mine starts that the Cataclysm has also affected underground creatures.
Add to this what Mark said about unforseen breeding complications in humans, the small remaining population, and mutated humans presumable difficulty crossbreeding, and I don’t see any way that we as a species make it through the Cataclysm. Maybe some mutated form of humanity survives, or is enslaved, but I just don’t see regular old homo sapiens getting through the apocalypse.