I think that's fair, but I think there are also a lot of people in this discussion who reject out of hand the idea of: "this person shouldn't ever be in a position of authority over people because their mental health issues cause them to act around those people in ways that end up being construed as inappropriate at best, and actively making people feel unsafe at worst".

A handicap might mean that you just can't do certain things. No, it's not fair, but it's not like we expect the a quadriplegic person to be a long-distance runner... at least not with the medical technology available to us today. I hear a lot of rhetoric (that I agree with) around how a mental illness should be treated just like any other illness and not stigmatized as something to be embarrassed about. But it goes both ways: if a mental illness is just like any other illness (or handicap), then it's perfectly possible that some mental illnesses might mean that some activities aren't feasible, at least not until we understand them well enough to provide better treatments.