A careful study of local state laws you will find a lot of states have blanket, no due-process prohibition for conceal carry application in terms of metal health issues. This ranging from disallowing someone having a conceal carry simply for being a diagnosed with a mental illness of any sort, to having been voluntarily entered a psychiatric hospital once, to explicitly listing certain illnesses that is irrelevant but can disqualify an individual.
I certainly won't think that a friend who went into a psychiatric hospital voluntarily when she was 18 for a eating disorder should be stripped of her conceal carry rights, especially if she reportedly was threatened by locals who wanted to teach her how to be "a real woman". On the federal level she did not even need to file a partition since it was voluntary. Even if it were not voluntary she could file and nothing could stop her from purchasing a handgun. Yet in many states the only time she could use it was for home defense. Not practical.
I have met lots of trans people and have quite a few friends. A lot of them do have to have some mental help one time or another, and of course, therapy is almost inevitably a part of their lives if they can afford it. This means the most vulnerable portion of our LGBT community that needed to conceal carry the most happened to be the most likely portion to have large percentages to be denied their right to carry based on outdated laws or laws based on ignorance or fear or stereotype.
I have no answer, other than mental health care reform, including the laws. This is the 2010s, not 1920s, a mental health institution now treats lots of illnesses that logically have nothing to do with firearm ownership. Eating disorder. ADHD, Alcohol Detox.
I am always against the idea of banning someone from owning a firearm because one is a harm to himself only. I talked with therapists and they would told me that there are other methods that people used to end their lives just as effective and quick. In a way, firearm is the more humane way. You can ban a person from owning a firearm but you cannot ban him from jumping out of his apartment window on the 3rd floor. Some of them can certainly overdose their own medications intentionally and you cannot ban them from owning their own medication either. I understand the need morally to stop someone from making an impulsive suicide, but on the other hand how do we really know if the person is impulsive? I am speaking as a person who lost a close friend through suicide. To this day while I mourn losing her, I did not disagree with her decision. Using a firearm meant she is no longer in pain now, and it broke my heart every time I saw her in pain and for each treatment it got worse: she wanted to commit suicide for a long time, and ultimately she did it with a firearm it really did not matter.
Finally The Federal level of course recognize this and you can always have your second amendment right restored by filing to the proper channel, but apparently on the state level there is no such thing. Since a lot of people or court consider conceal carry a privilege, not a right, we are now in a catch-22 situation. This is especially true if open carry were illegal in some states. Imagine you live in a state where you are denied conceal carry because of decades ago you went into a hospital to treat "gender dysphoria", but every single homophobe and racist and closet klansmen could get a conceal....