There are two sides to these discussions. I'm not segregating illness into any sub category - there's no need, sick is, well, sick. Broken brain or broken leg? Does it matter?
From the sick persons perspective, they are not feeling well enough to go to work, individuals have different points at which they cannot go to work. They could be the type who walk two miles through snow when they have a broken foot, or they could be the type who have a day off because the have a runny nose. Ignoring the clear slackers using sickness as an excuse, if people get ill, in most cases it isn't their fault.
From the employers perspective, sickness of any kind is a pain. It can cause general disruption, or possibly a business that suddenly grinds to a halt, or possibly even loses a customer because work promised doesn't happen.
if somebody is ill, they may decide they have to leave. Or, the business might decide they must go being a liability. It boils down to the facts. If somebody is a constant thorn in the side because they can't do their job, then at some point, the gears have to turn and they get replaced with somebody else who can do the job. It takes systems and policies, but this needs to happen. Clearly, the sick person feels they are being fired for being ill - something beyond their control, and in most cases, this is exactly what is happening. Jobs are interviewed for, with carefully written contracts. A job has to be earned, and somebody with a poor health record is more of a hindrance than somebody who is healthy. This is countered with the reliable, healthy but troublesome person set up against the unreliable but always helpful and useful sick person.
I've been in the position of having to get rid of a person with severe and frankly scary Schizophrenia. I've got no issues with mental illness, and I could have lived with it, difficult though it was. Imagine having a meeting with staff, designing and detailing a plan for the next day and then finding out it was wrecked because one person had no recollection of even being at the meeting, let alone doing what she said she would do? This person actually did something unforgivable, way above the usual gross misconduct - something with severe and perhaps irreversible implications for two other members of the team. She walked, immediately. However - I find the person on Facebook slagging me off for sacking her for being mentally ill!
I've had people with limbs missing, very strange attitudes and some with clear physical illnesses undisclosed on interview. They've all done fine, and the small changes we made to cope with their oddness perfectly doable. what I want are people who can do what they say they can do. I've had broken limbs, phobias, allergic reactions and loads of physical and mental illnesses - and if they are genuine, everyone copes. Two of these people often described themselves as being a bit mad some days. No issues with people knowing when they're not quiet themselves. Do they work hard and would I hate them to leave? yes. I can put up with all kinds of things when these people are worth it.
I cannot stand slackers or people who just don't even try to fit in.
Nowadays, we have to pussy foot around. The person I had to sack who had a totally genuine mental illness actually said to me one day - "now I've told you about my mental illness, you n' get rid of me. I know I am rude, and upset everyone and I don't care - I have a mental illness. Oh, and by the way you cannot tell anyone I have it". Advice from HR was to put up with it for the length of the contract. If I needed to get an extra person to cover her, then that was fine - so effectively she got a get out of jail card. Hands tied. I don't mind admitting that when I had to get rid of her for her really serious incident, I didn't feel bad at all because of the seriousness of it. I didn't give her a bad reference. I didn't tell anyone what had happened apart from the person concerned who needed to know to fix the problem caused, and HR. none of the others knew I had fired her - until she told them all she'd been fired for being ill. At this point loads of people came to me to tell me of things she had done, that because of her condition, they'd all put up with. A terribly abrasive person, and not just to me but everyone in her team. Nobody shed a tear.
I've had a quick count up and if you include conditions like ADHD, Asbergers, OCD and depression we have a bit like 50% physical and 50% mental illness in the team. A small team of males/females and we have thyroid, rheumatoid arthritis, damaged nerves, mild autism, lung degeneration/asthma with just one person having a clean bill of health at the moment. All of these are on repeat contracts, having completed them successfully and then coming back to do the same things again, year on year. however, in the past I've had loads of one contract wonders - useless people I do not offer a second one to. Not because of any illness, but because they take advantage, are skivers and wastes of space!