Speaking from a dance SM perspective...
1. Cancer - it depends on the kind. I worked with a dancer with breast cancer that turned into bone cancer. This is serious for someone who is dancing and causing major impact on joints/bones. Thankfully she shared the info with artistic staff so that choreography could be modified to work within her limitations. I also told her she had to tell our physical/massage therapists, as they need to modify the work they do on her body so as not to cause additional problems. Others have had "milder" forms of cancer that were eradicated with a few radiation treatments and they were right as rain in a few weeks. And for that, no one needed to know.
2. Strained Muscle - I have hidden this information from artistic staff before, as dancers don't want to risk not being cast. However, if the injury is due to work (and much more severe than strained), that's a completely different situation generally involving workers' comp. I have encouraged dancers to take it easy, rock tape body parts, get PT, and to be honest with artistic staff. Ballet dancers are trained from a young age to respect (and sometimes fear) the directors and teachers, so it's hard for them to be honest about issues that could limit their ability to perform.
3. Mono/Chicken Pox - As soon as I'm told, I tell them to stay home and that they cannot return to work without a note from their doctor. Dance is a highly interactive activity and any illness spreads quickly. I have to tell artistic staff why I told the dancer to stay home, but it doesn't go any further from there. As far as anyone else is concerned, the out dancer is "sick."
4. Herpes - About 50% of adults in the US have some form of Herpes. There may be people who have it and don't even know it. I think in this case, if someone has it and fails to disclose it, and is then cast to kiss someone else, the fault is on the infected person. If a performer tells you they have it, then it is your responsibility to make sure others are protected. While I have not experienced this situation, I would tell the performer to inform artistic to avoid any issues with spreading the virus - and warn them that if they don't, that I will inform them for the health of fellow cast members.
5. Pregnancy - I could see in the short term, this could be detrimental to an actress who is on a short contract. The AGMA dancers I work with have protections that allow them to be out for up to 1 year, and then they must be put back on contract (if they want to return). It's important for the costume shop and it's important for artistic to know any restrictions on their bodies. I've had 3 dancers get pregnant while on contract, and most wait until they've cleared the "danger zone" of pregnancy before going to artistic on their own. Though I am honored to be one of the first they tell, I do recommend they tell artistic ASAP so that they are aware and can make any casting adjustments necessary. I've had a choreographer create a role just for a dancer who was pregnant, so the choreography, character shoes and the costume were all accommodating of her changing body. And you could barely tell she was pregnant the way the costume was built. Worked like a charm. It can't be hidden for long, especially when performers are required to wear costumes built to their measurements.
6. HIV - I worked with someone who has HIV, and she made a point to tell me (PSM), union steward and the PM about her condition and what precautions should be taken if she gets cut/injured. She told us in confidence and there was no reason to take the information any further than who already knew. Generally her work was solo, without involving others during the run, and she was always cautious during load in and load out. The methods of spreading HIV are so specific, and as a technician, she wasn't going to be put in a situation to share any bodily fluids with anyone else. Granted, getting cut is always a concern, but the people who would be tending to someone who was injured already knew the situation, so I don't feel this had to told to anyone else.
Jumping to HIPAA - as a dance SM, I was in contact with our physical therapists, chiropractors and those treating our dancers for "first aid" treatments and sometimes workers' comp claims. It was a strange line to walk, as the doctors were torn as to what to tell me, as a member of management of the employing company. I would check in to make sure certain dancers were seeking treatment, if I already knew they were injured. It's been a while, but I remember one doctor telling me everything about the situation, and others being hesitant. Some would simply explain that the dancer was receiving a particular treatment and when they had been seen, but not the progress. And the last one wouldn't tell me the issue or treatment, but what he felt the dancer was able to do "can walk and mark, but cannot jump" kind of info. The last one may have been the safest, as I had to relay what the dancer was allowed to do, to make sure their healing was on track.