People with cancer are stigmatized because they have cancer; not because people call cancer yeneh machla.
If you compare cancer with other illnesses (pneumonia, hepatitis, etc.), it stands out for a few reasons.
1) It can affect the health of the patient in the future (think fertility, etc.)
2) It is typically associated with a long battle for survival with many ups and downs, which is more of an emotional roller coaster than many other illnesses would have.
3) In many cases (depending on the type/stage), it has a higher fatality rate.
4) It is more common than many other diseases.
Personally I usually call it cancer. Maybe I’ve become desensitized from all the people I know who have (had) it.