It's not only parasites, you also have viruses. Rabies, for example, manipulates the brain to induce what to me appears to be a highly specific response to a very specific thing : hydrophobia (see https://en.wikipedia.org/wiki/Rabies#Signs_and_symptoms , in particular the video).
And it induces the _same_ symptoms on a huge chunk of mammalian species. For all you think the human brain is different from that of say, a wild fox, the same mechanism used by this virus to introduce hydrophobia _works_ on both species' brains.
It's already amazing to me that you can manipulate different human brains in the same way and introduce such a specific response; the idea that it would even extend to different species... If you believe even for a second that brains work in any way like a neural network, this is just mind-boggling. How can you manipulate a neural network to suddenly fear water? How can you manipulate _different types of neural networks_ to suddenly fear water, in a generic way? You/the parasite/the virus can only influence the hardware/wetware, and not what the NN is trained on.
It's evident that it's not an easy task, not even for the virus itself, as it "fails" to work on around 20% of the infected, as per the wikipedia article, where it causes some strange lethargic behavior instead of the "intended" waterphobia. ("Intented" because it's definitely more likely to cause the virus to propagate than the lethargic behavior).