We are referring to domestic cats no doubt. What does the phrase ‘care about’ mean? To ‘care for’ someone would apply to a cat owner looking after their house cat. But the question asks whether cats have affection for their owner or other people who the cat knows because to ‘care about’ means affections for an animal or person.
Therefore the question is asking if house cats can genuinely have affection for a person? In order to do that domestic cats have to (a) have emotions; in fact sufficiently developed emotions to make close friends because they like another cat or dog or a person and (2) have demonstrated that they can make friends and close attachments to others.
The house cat passes on both (a) and (b). Experts and observant cat owners would all agree that domestic cats have emotions. The only debate is how complex their emotions can be. A cat’s emotions are certainly sufficiently developed to have affections for another cat or person.
We often see cats curled up together snoozing or demonstrating a fondness for each other in a variety of ways. Of course cats demonstrate their affection for humans they like and know well by lying close to them, head butting them, exchanging scent with them, purring around them, lying on them, licking them and clearly enjoying being near to their human companion. These are all clear signs of affection for their owner and there are many others personal to the cat and their owner.
Sceptics would say that the domestic cat is merely acting on instinct and responding to their owner because they are fed and made secure by him or her. But all the signs indicate that it’s more than that. As stated cats also feel emotions. We know it now.
The human to cat relationship is an interspecies relationship. There are many examples of domestic cats having relationships with other animals such as horses, deer and dogs to name three. In each case there are clear signs of a meaningful relationship underpinned by genuine affection based on emotions.
The conclusion I have to the question in the title is Yes. However, we must always remember that the house cat is a cat and not a person.