My understanding is that John F. Kennedy liked cats and animals in general but deliberately avoided being photographed with a cat during his presidency because he was concerned that some people regard cats as sly, devious and even evil. He was aware of that perception by the voting segment of American society and needed to protect his image. I stress that that is my understanding of the situation regarding John F. Kennedy and cats.
He did have a cat who was named Tom Kitten and it appears that he was a single colour grey (solid color). The White House Historical Association refers to the family of John F. Kennedy bringing Tom Kitten to the White House with a canary called Robin and pet hamsters called Debbie and Billie.
There are photographs, albeit quite rare, of John F. Kennedy and cats (all before his presidency?) but I couldn’t find one of John F. Kennedy with Tom Kitten perhaps for the reason given. I have seen a photograph in a book and therefore cannot reproduce it here of Jackie Kennedy, his wife, and their daughter Caroline with Tom Kitten. Mrs Kennedy is smiling animatedly and was clearly happy while her daughter also appears to be content.
The photograph on this page of Mrs Kennedy and her daughter is another one. Tom Kitten is the cat on the right while the tabby cat in the middle apparently was not their cat.
Also, on this page there is a photograph of JFK when he was much younger holding a kitten while visiting the Solomon Islands in 1943 (see above). The photographer is unknown. The picture indicates that he was at least comfortable around domestic cats and perhaps more than that: he liked them. And that is what I have gleaned from a book by Dr. Bruce Fogle, a veterinarian and author who has written that he did indeed like cats but was concerned about the image that they portrayed to the public as mentioned above.
The fact that they had other pets also indicates that the family liked animals in general. This is what I would expect of JFK and his family. The book referred to is The Encyclopaedia of the Cat.
SOME MORE ON CELEBS AND CATS: