Unfortunately, there are still many bosses who would be put off by a mental health issue in someones past though.
In a former role, I interviewed a candidate who cited burnout as one of the reasons for a career change a few years earlier. After the interview my boss (who was in the interview) made a big thing about how that put him off. I think it was his main reason for rejecting the candidate.
It is important we do talk about these issues though. At the time I did not feel able to say "that's not ok" to my boss in the same way that I might if he had been put off by the candidate's sexuality. I should have.