O boy, plus shampoo, other hair and body products, toothpaste, denture cleaner, leftover drinks (tequila, scotch, beer), laundry supplies, dishwasher stuff, etc. Let’s not forget most people toss feminine and latex products too."Such an environment"? It's a tank. Heavy stuff settles (i.e. kitty litter). Grease and fat floats.
The content of the tank is crap and piss and toilet paper (should be anyway). What do you think could react with kitty litter than would make it float, not to the surface mind you (the outlet has a tee to prevent floatables like grease and fat from entering the drain field) but to a few inches below the surface of the water, enter the outlet, to the distribution box, float in there, and then clog the 5/8" holes in the 100' or so of perforated pipe making up the drain field?
As you mentioned, kitty litter is inert, so bacteria won't break it down (but it will sit at the bottom of the tank waiting to be pumped out) and as someone else mentioned previously, kitty litter is made of clay and hardens.
If the OP had said they'v ebeen dumping kitty litter for a long time, I'd agree with you. But since it's one time, the septic is fine (assuming they're on septic).
100’ of line per what combination of bedrooms and bathrooms?