manta49, it wasn't that long ago that homosexuality was considered a mental disorder.
Should being gay prevent one from owning a gun?
The thing is, once you put in mental health requirements, per se, as opposed to specifically identifying issues that should prevent firearm ownership, it is up to whoever gets to write the rules.
If those persons think that supporting Manchester United is a sign of poor mental health, or that opposing their political party is a sign of poor mental health, or - dare I say it? - that wanting to carry a gun is a sign of poor mental healt...
So the onus should be on the government to prove and specify what exact "mental disorders" would be real threats, and to further prove that an individual actually has such.