The full faith and credit clause was written primarily to preserve judgments across state lines. That way a party can't just run off to another state to escape enforcement of a judgment rendered. Its use has since been expanded to marriages (traditionally this was always the case), child custody orders, and protection orders (to name a few). Gun permits have not been included yet. You would need the Supreme Court or Congress to take a liberal (read: broad) view of the clause once again in order to get a court decision or some legislation through in order for this to happen.