We have two cats, both 2 years old, and a 1-year old dog. Our neighbour has found pee and poo on her bed and thinks it's our tortie as she has sometimes wandered into their house.
Why would our healthy young female neutered cat that hasn't weed inside since she was a kitten do that in another house? There are quite a few other cats in the neighbourhood, so I was thinking that if they're getting territorial, she might be trying to mark her own territory in a house with no pets. In recent weeks we've had another cat come into our house to eat the cats' food, so perhaps our cat feels threatened.
Neighbour is being totally reasonable, btw. I've given her some repellant spray, she's going to keep the windows closed (we're in NZ so it's hot), and she's going to spray our cat with water if she tries to get in again.
We did have issues with our cat last year when we got a dog, and she was suddenly very skittish, but a few months of a feliway diffuser sorted that out.