“It is not legal to sell guns to violent felons (or any felons) or mentally ill people.”
In most of the us, if you don’t KNOW if the person is a felon, it is legal. And as you point out, there is no way to easily find out unless you are a licensed firearms dealer. Universal background checks are needed.
“this does, in effect, remove someone’s rights without a trial or conviction of any sort”
Which is why there needs to be a way to get off this list. Just as there needs to be a way to appeal your denial of a gun permit. This is not complicated!