The NFL is a franchised business. Like most franchised businesses there is a vetting process for buying a franchise. The league has the right to reject him based on this or his other past transgressions (e.g., illegal drug use). I think, it would be a mistake not to consider the views of the players union.
In my opinion, Rush is a racist. Further, he has allowed race to color his views on the very sport of football. Rush has the right to speak his nonsense and others have the right to criticize him and choose not to associate with him based on his words/actions.
The NFL is a franchised