It's entirely an individual thing. I own multiple firearms, of a wide variety. I definitely show a preference for World War II and Russian-designed firearms, though. I also have the mental conditioning to use them properly in an emergency. I have planned, considered scenarios, and know each of my firearms intimately well, and, most importantly, I have firm rules established for things I will NEVER do with a firearm or any other weapon. Frankly, I am probably more qualified to own and utilize firearms than even the vast majority of NT's. I have my rules and procedures already laid out, and that's far more than 99% of firearm owners can say, including many law enforcement officers.
However, there are aspies who should probably not own firearms, just as there are NT's who should probably not own one. I've known many people I wouldn't trust with a gun, and Asperger's, by itself, makes little or no difference. In my case, my autism makes me a safer gun owner because I am big on rules and procedures. There are things I will not do, and lines I will not cross. To someone else who has significant motor impairment or another condition affecting judgement, it is something they need to think long and hard about.
In short, no. Asperger's should not, by itself, ever be a disqualifier from owning guns. It is not a mental illness, nor would it impair judgement in a life or death situation. Sometimes coexisting conditions or extreme traits can cause significant impairment to a person's ability to responsibly possess a firearm, but Asperger's by itself does not.
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Heart of the guardian, way of the warden, path of the exile.