What would cause a bloody, mucousy stool for only one time?
I had the same problem. Three cats, every once in a while we’d find a bloody stool in the litter box. the vet said we could get a bunch of expensive tests done, but they also said it could happen for any harmless reason. Changing the food (which you say you haven’t done), stress, even past worms. If the cat ever had worms, the treatment kills the live worms, not the eggs they could have lain in the intestines. Then when the eggs come out or become worms, it tears the intestine a tiny bit, equaling blood. If it doesn’t happen that often, and both cats are acting normally, I wouldn’t worry about it at all.