There was an appeal process set up for special cases, such as a guy who was convicted of the equivalent of a felony in Mexico for accidentally taking a small amount of ammo into that country. But he cannot appeal or get an exemption because the review office is not funded.
I'll keep my Constitutional reservations separate about a federal sanction on 2nd A rights upon a STATE felony conviction.
You know, I don't really have a problem with this providing the felon has finished his sentence i.e. is not on probation or parole.
Note, that serious crimes result -- or should result -- in decades long sentences. OTOH, a kid nabbed for stealing a car at 18 is a convicted felon even if he owns a string of businesses and is a deacon in his church at age 35.