To begin, I must state that I do undoubtedly believe that novels/ the novel inspires empathy for many reasons, and originally I disagreed with Lynn Hunt's hypothesis but after thinking about personal experiences I do have to agree that I believe that novels did have a hand in the growth of human rights.
Have you ever watched a movie (or read a book) with a main antagonist, and originally all you felt for them was distain because maybe they killed a bunch of people or were plotting something horrible, or maybe just rubbed you the wrong way? Has that movie (or book) later overturned your feelings towards the antagonist or character because you learned their backstory, or motivation, or the pain they were suffering? I know I have had more than one experience with this. For example, Maleficent. In the original Sleeping Beauty she was made out to be a horrible monster that aimed to kill the princess and force everyone around her to suffer, but, in the newest adaption of the story we learn that the kingdom of which the princess lives tortured and destroyed her home... thus giving her understandable motivation for her actions.
Novels and movies can create a feeling of empathy in a reader/ watcher towards a character they usually would not feel empathy for. Hunt goes onto explain that "people learnt how to empathize across more distant social borders than ever before." I agree with this because without these works the most you can do is try to persuade people to feel empathy before them, which is not as easy as it sounds... especially when the audience is not as willing as they should be.
These novels can make people rethink opinions, values, and beliefs that have been systemically drilled into their minds since they were children. For example, if a bigoted man grew up in a society where people of a different skin colour, sexual orientation, or gender were lesser than him (or plain outright did not deserve the rights he had), possibly the best way to revitalize him and persuade him would be to show him that people who are different than him still share the same feelings, and like Hunt quoted "others have selves too."
So yes, I am convinced by Hunt's argument that novels do indeed influence the growth of human rights!