Nope! The cats don't come for a while if you don't set food out, but they always come right back when you set food out again. Overall an extremely stress-free experience for cat lovers.
One of the cats, Hermeowne, is obviously Harry-Potter themed (the author is infamously a TERF and the books have a lot of racist undertones), but you can change their name to something unrelated. Otherwise, not at all.