An Op-Ed by Peter Mandel underlines some of the concerns about a blanket ban on those will "mental illness". 

Via WSJ: 

I am mentally ill. I won’t bore you with the details, but I’m one of hundreds of thousands of Americans with a tough-to-treat, life-affecting neurosis known as obsessive compulsive disorder. Since I happen to live near a leading psychiatric hospital, I’m one of the lucky ones. I was diagnosed as a young man. I visit my psychiatrist regularly and take a medication at the beginning of every day. I’m in the “functional” category. I have a family and work for a living, though I don’t earn much. I even own a home...

...As it happens, I have no interest in owning a gun. But what if I did? Should society stop me? In the current debate following the Parkland massacre, there are many—including the president, moderates in Congress and even some gun-rights advocates—who say so.

If you agree, I have to ask: How will you go about this? By some edict from my doctor? Even if he were inclined to sign one, which I doubt, do you not realize that I could easily obtain a second opinion?

The idea of stripping rights from the mentally ill is a very slippery slope. Rarely are we sufferers institutionalized or restrained nowadays unless we’ve harmed ourselves or others. Want to label a few of us as “dangerous”? We’re as hard to decipher and diagnose as anyone you know.

Those, like me, who suffer from mental illness come in millions of different degrees of severity and functionality. Experts these days talk about patients not as having autism but being on the “autism spectrum.” Is there an obsessive-compulsive spectrum, too? A spectrum for every disorder?

Read more here.