If a person had the personality of a domestic cat a doctor would diagnose him as autistic or having Asperger’s.
That should answer the question in the title. What I’m saying is that the behaviour of cats and humans is different (obvious). People consider the domestic cat to be a bit aloof and independent et cetera. This aloofness and independence can be interpreted as being a personality disorder, one in which the cat has difficulty relating to either his human companion or other cats.
I mention this because both autistic children or adults and people with Asperger’s have difficulty relating to other people. That is one of the symptoms.
Ultimately, it is about perception. It is about our perception of our cat’s character and personality which we compare to the personality of humans because we treat our cat as a member of the family and we anthropomorphise our cat. This is all perfectly normal but in humanising our cat we can end up measure his/her personality against the personality and behavioural characteristics of humans at which point it looks as though our cat is autistic; hence the question in the title, which comes directly from the Internet. It is a search term used by many people. Accordingly, I have to conclude that some people genuinely believe that the domestic cat might be autistic.
To the best of my knowledge, cats cannot suffer from Asperger’s syndrome or be autistic. To think that they do is anthropomorphizing your cat. Although, in discussing autism and domestic cats we are touching on the topic of the mental health of domestic cats and whether they can suffer from the same sort of mental health issues that humans suffer from.
The answer is that we don’t know but, as far as I am concerned, it is unlikely because cats behave naturally and instinctively. A lot of human mental health issues originate in human-generated unnatural situations, distortions and behaviours. Humans don’t behave instinctively most of the time. Jackson Galaxy in the USA believes cats can suffer from mental health issues and that drugs can be usefully prescribed.
P.S. Cats can suffer from apparent depression if suffering from chronic illness or a permanently hostile environment.