I've met people like that. . .I won't say mentally ill (well, I don't know them personally, but by the description and based on the people I've known). It's more of a, hmm, denial, maybe? Ignorance? Learned helplessness? They don't know what proper care consists of, what healthy animals look/act like, and don't have the gumption to do anything about the conditions even if someone spells it out for them. You could maybe call it a mental illness, but it's something that could be treated.