Here are a few quotes from this article in the Des Moines Register about whether Iowa should be granting gun permits to blind people, as it is currently doing. As you can see, opinions vary:
Although people who are blind can participate fully in nearly all life’s experiences, there are some things, like the operation of a weapon, that may very well be an exception.
Patrick Clancy, Superintendent
Iowa Braille and Sight Saving School
There's no reason solely on the [basis] of blindness that a blind person shouldn't be allowed to carry a weapon.
Chris Danielson, Public Relations Director
National Federation of the Blind
I'm not an expert in vision. At what point do vision problems have a detrimental effect [on firing] a firearm? If you see nothing but a blurry mass in front of you, then I would say you probably shouldn't be shooting something.
Sheriff John LeClere
Delaware County, Iowa
When you shoot a gun, you take it out and point and shoot, and I don't necessarily think eyesight is necessary.
Imagine me with a gun. It's just crazy.
another blind person
Is it, Mr. Wonder? Or is it just … <looks into camera> … very superstitious?
The legal issue, or at least a legal issue, is whether an Iowa law that requires officials to issue permits in most circumstances also applies if the applicant is blind. Some people think that to deny a gun permit merely because of blindness is illegal discrimination. Others note that disability accommodations usually need only be "reasonable," and also suggest there is value, and maybe even an important public safety interest, in making sure that gun owners can actually aim before blazing away.
Personally, I'm with Stevie on this one. I don't think anybody argues it's unreasonable or discriminatory to deny a driver's license to someone on the grounds that they can't see where they're going, so I'm not sure why it should be any different if someone can't see where he's shooting.