Actually, the 2nd Amd, being absolute does not make exceptions for mentally unstable people so long as unstable people are people. The only exceptions could be under the involuntary servitude provision of the 13th amendment, in other words incarcerated prisoners, maybe.
I know I’ve seen, and you probably have too, some folks who I, or you, may think should never be allowed around a firearm. But, that ain’t my call as long as they are citizens. More training required.