My guess would be that a non-Caste System NFL would probably mirror the current NCAA College Football racial makeup. From my understanding Whites make up about 45-50% of College Football rosters (If I am incorrect about this please let me know as I am not totally sure!)
As we see in alot of College teams, Whites can play all the positions like CB and HB and this would be reflected in this hypothetical scenario.
There would be alot more Jason Sehorns and Craig James out there.
The reason why I don't think the White ratio would be higher is that Whites enjoy a vast array of different sports. Hockey, skiing, biking, golf, tennis, gymnastics, swimming, etc... and with so many folks playing all these other sports it reduces the number that play football. Whereas blacks, generally being poorer, don't have the money to buy the expensive equipment some of these sports require and gravitate more towards basketball where all one needs is a ball and a trash can nailed to the fence or football where the team ususally provides equipment.