I also believe that someone with a felony who has already disregarded the law and didn't have respect for his fellow human beings is more prone to showing disrespect for their opponents.
Sure, someone can be rehabilitated, but should the NFL be that second chance? No. The NFL has taken player injuries, especially concussions, seriously under Roger Goodell's leadership. I think having players who've been shown to disrespect opponents or civilians should have no place in the game.
The other reason that I feel this way has to do with money. The NFL is being sued left, right, and center these days by ex-players due to injuries they sustained during their playing days. If a felon were to seriously injure an opponent, could the NFL be sued by that player?
I'm guessing it will open the NFL up to future lawsuits. An injured player could claim that the NFL knew of the player's violent past but disregarded that information and put NFL player at risk.
I think that there's too much at stake in the current NFL for the league to allow individuals with violent criminal pasts to be allowed to play at this level. I know that's probably not a popular opinion, but that's how I feel.