That's a great point. There is one cancer though that doesn't attract sympathy -- that is lung cancer, where the first comment will often be the question 'did you smoke'. Per death lung cancer research is funded at less than 1/10th that of breast cancer, for instance, and this is true world wide, so there are big repercussions from the social stigma of having lung cancer beyond a lack of sympathy. I once went to a support group for cancer patients and opened up about having lung cancer, then another woman later said she 'didn't do anything to deserve getting cancer like you (I) did' looking right at me. So the lack of empathy even extends to other cancer patients.

Cancer patients are otherwise seen as being blameless, whereas with mental illness there is the underlying bias that it is due to a moral or other failure of the person -- maybe not the illness itself but the symptoms.

There is also a lot of fear of the mentally ill and the overlap with the prison population is significant too. And the point about the mentally ill often being unlikeable is also on the mark. Another issue is that cancer is in some cases curable, or it goes into remission, whereas no one talks of any cure for mental illness. I think the fact that it is uncurable is a big factor in the lack of sympathy.