The cat poop, yes.

The clumps of clay/litter/urine ... it depends on what they are using to make it clymp. The plant-based (corn, sawdust, paper) ones that use corn starch polymers decompose quickly. The clay-based ones don't, and leave lumps of clay ceap in the sompost.

I toss the pee balls in the compost fairly regularly.
Here's why.

I put a pee ball in a bucket and added water to see what happens. It turned to foggy water.

I looked up what is in my cat's litter. It includes potassium, similar to a product gardeners purchase by the bag.

I never have enough nitrogen for my piles.. pee is a perfectly good source.

Less stuff going to the landfill to be buried for future generations to deal with.

And last but not least.. my cats prefer one box to poop and one to pee. I have no idea how or why that happened. One of lifes little mysteries.

Thumbs down on the poop. I turn my piles and don't want to revisit that. ick.
Plus too much mental energy to remember where poopie compost ended up over time and what if I change my mind and want to add a veggie/herb or something?

Yaa for pee balls. :)

While there are many people that do put the feces as well as used cat litter in their compost no one with knowledge of the damgers would advise doing that. Because the pets, dogs and cats, live so close to us they are potential carriers of many disease pathogens that adversly affect humans as well as many that affect them and could infect us. From cats that is always Taxoplasmosis and from dogs many others that some dismiss because they have not known anyone that has had these diseases.

Without going into the science of kitty-litter, if one removes the clumping offender, kitty litter is fine to add to your compost pile.
Ninety-five percent of k.l, is clay, the kind that absorbs moisture and is probably as good as putting peat moss into the pile.
Urine has proven to be not harmful when given to the compost pile so any residue of liquid in the litter is also a good addition.

I'm from MO, show me the man who has taken ill from whatever the compost has made contact with him.

I'll try putting some in water and see what happens. In fact, I'll even water a houseplant with the water to see if there is a detrimental effect. It can't go in the toilet because we are on septic and it is hard for me to find a place to dump it that the dogs don't find.

And yes, I agree that getting sick from touching any sort of pet excrement in garden soil is a stretch. Too many important things to worry about.

I went and found an older thread over in Garden Experiments for you. A quick scan now shows it is one that had some interesting links to information.

Oh, and be sure the house plant water is diluted enough, since high nitrogen can burn roots. But you undoubtedly already knew that, I just feel the need to throw it out there.

Here is a link that might be useful: these people are a little too much into kitty poo