They really wouldn't wear them around HIV, Hep (A,B, or C) or papilloma patients. None of those viruses are airborne.
I'm including an article on how masks work to prevent viral transmission (without being 100% effective). I'm sure you've seen others like it, but give it a read and an open-minded think. The source is not a news agency, it's a teaching hospital.
https://www.ucsf.edu/news/2020/06/417906/still-confused-about-masks-heres-science-behind-how-face-masks-prevent
Also, the name of the game in public health is something called Harm Reduction. Masks, condoms, seat belts, hand-washing, medical checklists, needle exchanges and smoking cessation campaigns are all stellar examples. The goal isn't to make a perfect, disease-free world, it's to introduce interventions that effectively reduce the total pain and suffering. And it works.