My impression is that if the condition involves quiet angst, everyone will sympathize -- but if it's about real heavy duty craziness, no one wants to hear about it (or look at it or think about it, etc.).
Try having a casual office conversation about how you were sick last week. Compare the tenor of the conversation when the sickness is 'the flu' versus 'depressive episode'.
Every mental illness is stigmatised, it's just that some are more stigmatised than others because they're 'louder'. Part of this is due to mental illness being really hard to understand if you've never been exposed to it (as a sufferer or a loved one of a sufferer).
Stigma is almost entirely a cultural thing: I know of someone who's first manifestation of mania (bipolar disorder, type 1) was in a religious setting... so when she said she heard God talking to her, they were reportedly thrilled. It didn't come out that it was a problem until she was on the plane home and was blessing the passengers (edit: details slightly obscured/changed).
That really got me thinking about how deeply "aggresive confrontational competition" infects our intuition about the world, even in supposedly collaborative environments.