Not sure why it's scary? In NZ we've got bovine TB, and you need to learn to identify it in animals you're butchering, deer can get it but wild pigs are more prone due to their predilection for scavenging carcasses - brushtail possums, an introduced pest from Australia, are the main vector for cattle, deer and pigs.

When I started hunting, I was taught, "don't eat the lumpy ones", and of course, always make sure you properly autopsy the animal, liver, lungs, heart etc. And if you shoot a TB infected animal, don't transport the offal (especially not the heads of pigs, for some reason bovine TB has a predilection for their jaws), and bury or burn it if you can to prevent scavenging and further infection.

https://ospri.co.nz/assets/Uploads/Documents/TB-Information-...

To the best of my knowledge,human infection by bovine TB in NZ is very rare since the introduction of pasteurisation, although large pest control efforts (using a controversial (with some) poison) are undertaken to control the brushtail possum population.

But I dunno, maybe we gut our deer differently to how they do in America or something?

As a Kiwi hunter, what scares me disease wise about American hunting compared to ours is the ticks the animals typically carry - and the ticks in the forests!