The NFL has been trying to market their product for decades as family entertainment. The NFL's players are marketed as heroes / role models to kids by both the league as well as advertisers. So in keeping with the spirit of what the NFL is trying to sell, they should be trying to make certain that their players walk the walk. In many cases a lot of professional athletes and public figures have obligations in their contracts called morals clauses. This includes language about the personal conduct of the player and how it may reflect upon their employer. Clauses like these are very common, and they often have provisions built in for potential criminal activity.
The actions of these NFL players have hurt the image of the league. Especially if they're involved in violent felonies. And when it's domestic abuse? That's even worse. Part of the reason for the outrage? Player suspensions, like the one for Ray Rice's domestic abuse issue, were only for 2 GAMES, as this incident had initially been judged by the NFL. Contrast that with a player who tests positive for marijuana use. That carries a 4 game suspension.
The situation with Ray Rice seems to be the worst. Not because of Rice's actions, which are completely deplorable. But because there is the possibility that the NFL was aware of just how violent the incident was and may have moved to cover it up. There's an old adage regarding a scandal: the initial crime or wrong-doing is usually bad, but the greater sin seems to be the coverup.