Allow me to simplify; don't compost the feces of ANY animal that incorporates meat as a major part of it's diet. While it will break down, it takes more than is usually found in the standard compost pile.
So where is it "supposed" to go? You think it's safer flushed into the sewer system or in a landfill? At least in a compost pile it's breaking down and getting dispersed into a large volume of eventual humus. And if you think in any other circumstance such as landfill someone is taking care to eradicate those potential pathogens, think again.
Think of a forest floor -- the healthiest soil you'll find on the planet. It's composed of, among other things, rotting carcasses, the detritus of all manner of meat-eating animals not even buried where the heat is generated and other things you're not "supposed" to compost.
If you've got a cute little cubic yard container, you're composting mostly feces and harvesting humus in 90 days or six months you're in trouble. If you're creating large piles of diverse materials which are mostly plant-based
by many multiples and which reach high temperatures and have long decomposition and aging cycles then you're doing more to eradicate any potential pathogens than just about anyone else short of a municipal sewage treatment plant.
I sheet compost my dog's stuff in my landscape and I've added some to my compost piles. I also use the humanure that I generate when I'm outside gardening. They get buried in piles that decompose over at least a year and more likely 2 since I maintain 4 huge piles and it takes a while to get around to breaking each one down.
I'd compare my soil to anyone's. And there's never been any disease at my house other than the standard colds and "ickies" despite the fact that my humus goes into my veggie beds and around my fruit trees as well as my landscape.
