What negative effects does cannabalism have in other species (like prion diseases) and how are they mitigated?
First, to be clear, the very act of cannibalism does not cause the development of prions, but the consumption of an animal infected with a compatible form of them, particularly when eating nervous or digestive tissue (i.e. the brain, spine, stomach, or intestines).

To directly answer your question, yes, there are other animals that are susceptible to prions diseases when they consume infected members of their own species, or members of compatible carrier species. In the late 80s and 90s, there was a moderate epidemic of Bovine Spongiform Encephalopathy (Mad Cow Disease) that was concluded to have been caused by including bovine parts in cow feeding stock.

A common defense that I know of against infection from the consumption of infected animals is to simply not consume them at all. I know it's not really the answer you were expecting, but indeed, many animals have an active aversion to corpses, notably perceiving the smell of Cadaverine and Putrescine as repulsive. Evidently, a great defense against disease is to just not eat dead or dying things.

I've never heard of insects or arthropods having neurodegenerative prions, and wasn't able to find anything alluding to them having them, but I wouldn't be too surprised if they had other prion diseases that were infectious between them.

Sources:


Matravers et al. FST (2001);17,1-19


Also available at The National Archives

Cadaverine on Wikipedia
Putrescine on Wikipedia
Sacculina on Wikipedia