This will not be a popular opinion, nor is it a nice opinion, but sometimes the truth is neither and I think it is valuable to be explicit about these things sometimes.
The "stigma" against mental illness makes sense in a lot of ways.
I do not mean: that the mentally ill deserve fewer legal rights than others, deserve any kind of bad treatment or violence or ridicule, shouldn't be "accepted", or bear any "responsibility" for their condition.
I do mean: life is full of subtle social contracts that mental illness often causes people to flout. Mental illness (in many cases) makes people less predictable and reliable. Harder to deal with.
Some people reading this will say "obviously that is true, which we all acknowledge but have no reason to dwell on, and that is why it is a complex situation that demands awareness". Others will say "that is false and you are a bad person". First group, I refer you to second group.
If you are 100% committed to the goals of your organization (growing a startup, winning a war, whatever), you will be very hesitant to add a mentally ill person to your team/company/platoon. This makes sense. It sucks. Being mentally ill sucks. This is one of the ways.
That doesn't necessarily mean anything needs to or can be done to change it.
Also, it is possible that acting is a profession unusually accessible to people with certain mental illnesses.