I make a distinction between infectious and contagious diseases.
There are a lot of infectious diseases that I don't worry about, especially the blood-borne and venereal ones, because they're so easily avoided. AIDS, Hepatitis C, syphilis, etc., etc., etc. Bacterial endocarditis falls in this category for me BTW.
But then there are contagious diseases, and especially the airborne contagious diseases scare the heck out of me. I would not care to have antibiotic-resistant TB. I don't even want strep throat, a cold, or the flu. So, patholigically insensitive fellow that I am, I tend to avoid being around sick people and wouldn't care to work in a hospital.
A hospice would be a different deal, depending on what folks were dying from. I would consider cancer and AIDS patients to be no risk at all, but wouldn't want to be around the patient dying of TB.
You might want to consider doing volunteer work at a psychiatric hospital or rehab unit. None of the mental disorders are either infectious or contagious.