Hello Odysseus: Just because people are educated doesn't mean they're "enlightened". I never worked in academia. But, from what I've read, my impression is that it can be a "dog-eat-dog" environment. Everyone is scraping for tenure, & any little thing can knock you out of the running. At least this is my impression.
I would guess that your professors may see you as a threat to their careers, regardless of whether or not they understand your mental illness. So their intention is simply to keep as much space between you & themselves as possible. And, unfortunately, there may not be much you can do about that either.
I don't know how close you are to graduation. Is there any possibility of transferring to another school? Or could you transfer, within your present school, to another similar department that would allow you to continue to pursue your current educational goals but with different professors?
I'm sure none of these suggestions is anything you particularly relish. However, the reality of the situation may simply be that you won't be able to get letters of recommendation from the professors your mental illness burned. Otherwise, the only other thing I can think of is to try to establish relationships with other academic staff from whom you could get recommendations. This might include student counselors, placement office officials, or perhaps professors with whom you might be able to do some independent study. Just a few ideas that pop into my head. My best wishes to you...