It is a known risk:

> To date, there have been no reported cases of CWD infection in people. However, some animal studies suggest CWD poses a risk to certain types of non-human primates, like monkeys, that eat meat from CWD-infected animals or come in contact with brain or body fluids from infected deer or elk. These studies raise concerns that there may also be a risk to people. Since 1997, the World Health Organization has recommended that it is important to keep the agents of all known prion diseases from entering the human food chain.

https://www.cdc.gov/prions/cwd/index.html

I did not realise monkeys eat meat. Which species is that?

Even horses eat the odd bird.

Plenty of monkeys will opportunistically consume things, and some groups like the baboons and mandrills are gleefully omnivorous and have been known to take down small antelopes. Take a look at those canines and wonder not.

I don't think it's about believing one way or the other. Hunter ed warns you about this and recommends precautions.

But also consider that millions of deer are hunted and consumed in the US every year, and that hunters don't seem to be developing prion diseases at an elevated rate. We know relatively little about prions, but it seems likely that humans are fairly resilient to this, perhaps except for some predisposed individuals. Genetic factors are suspected, but there's no smoking gun. Acquired vCJD is exceedingly rare too.