You don't reconcile them. Driver's licenses don't, you just say one is good in all even if it is easier to get in another state. Problem then might be that non-resident permits go away but any of us in shall issue states wouldn't need non-resident.
Is it federal law that one state must recognize another's driver license? Not arguing, I really don't know.
As Rookie says, it's the 2nd Amendment, I'm a big states rights guy until it comes to the Constitution, it has to be the supreme law of the land otherwise the United part is pointless.
See my argument above.