Such restrictions are specified in state law. In my state anyone convicted of certain specific felonies within a set prior period of time cannot own a gun. Anyone convicted of a felony involving involving a gun cannot own a firearm period. Why should another state's laws override ours?
I wasn't saying they should. Federal statutes, however, forbid firearm ownership by anyone convicted of a crime for which they could have received 366 or more days in prison, as well as by many people who aren't even alleged to have committed any crime but who have sufficiently vindictive ex-spouses.