Possession of a hunting license is not prima facie evidence that the possessor intends to hunt. Nor is it definitive evidence that he is in possession of a firearm. Consequently, the two activities -- owning a hunting license and being a felon -- are completely compatible under law and logic.
On point: My daughter has a driver’s license but does not possess a car.
Heck...you’ve got to have a hunting license to trap.