I am seeing two different kinds of objections here.
One is pragmatic - "there shouldn't be a mental health exclusion because it will be abused by the antis to deny RKBA to people who would otherwise be appropriate candidates for RKBA."
The other is idealistic - "RKBA is inalienable, and should never be denied to anyone for any reason."
The idealistic version is unconvincing to me. Clearly there are some people who cannot be trusted with full adult rights and responsibilities. My grandmother's brother, for instance, had severe Alzheimer's and became very hostile, paranoid, and irrational for a while. His family took his guns away from him; rightly so. Folks above I suppose would say, "Well, don't Alzheimer's patients have a right to defend themselves?" I would say my great uncle was not competent to have adult rights and responsibilities, so at that point he has a right to be cared for by people who are competent adults. The family took his guns away, along with his drivers license and car keys and a number of other potential means of hurting himself or others - but they also took the responsibility for protecting him and taking care of him.
Similarly, anyone else who is permanently and severely mentally impaired, to the point that they are not responsible for their actions, should be cared for in a safe and humane way, while "securing" them from harming themselves or others.
Legally and ethically, a person who is so impaired as to be not responsible for their own actions is a clearly and distinctly different phenomenon than a person who seeks treatment for depression and anxiety. In a perfect world, we really shouldn't have to worry about overspill between these two categories.
However, this is where we run into the "pragmatic" objections. This isn't a perfect world. In this world, I am more frightened of the nanny-state autocrats than I am of the mentally defective people. Cho killed 32 people, which would have been less if people could have shot back at him. Stalin killed 20 million; the extent of his autocratic power ruled out any possibility of "shooting back" at him.
Some people too crazy to have guns? Definitely.
Any government I trust with the power to make that call? Nope; not this side of the second coming.