As for "Shall not be infringed" to be true, which of the following do you accept as OK to buy a gun?
Someone as they are holding the gun they want to buy saying this perfect for shooting up a school?
Should a non-US citizen/openly proclaimed ISIL member be allowed to buy guns?
A serial rapist with a felony convictions?
Mentally unstable people?
A meth head clearly under the influence at the gun shop?
If someone makes a threat with a firearm, it's a threat. Those ain't com under a number of other existing laws, because that violates the basic rights of others. Didn't matter if it comes via a rifle, baseball bat, broken bottle, pipebomb, or bare knuckles.
If a non-citizen is here legally, then yes, they should be allowed to purchase a firearm.
If we feel that serial rapist was rehabilitated to the point where they can be allowed to rejoin society (and realizing that this should be an incredibly high bar to clear), then they should have full rights restored (voting, gun ownership, whatever). If we (society) can't trust someone with legal gun ownership (or the right to vote, or any other basic right), then they need to be locked back up because they're going to find a weapon if they so desire.
Mentally unstable people shouldn't be free to roam if we can't sell them a gun, because they can find guns or any number of other ways with which to cause harm to themselves or others.
Drugs + guns don't mix, but that's also true of alcohol, fatigue, or stupidity, and we don't try to regulate the shit out of those things in an ineffective and intrusive manner.