They should not be exempt. This is because when one person hits another person they should be punished for it. Athletes are so used to getting special benefits that it's sickening. They should make an example out of Greg Hardy and completely let him go. No one needs to look up to criminals.
I don't care who Greg Hardy is, if he did this then he deserves to pay for it. Domestic violence shouldn't be tolerated and I don't care who is committing it. Sports figures shouldn't go around thinking they are above the law, because they aren't. I say if he did commit domestic violence then he should be suspended.
It don't matter who did it, it is a crime and nobody should be exempt from it. I think there need to be serious, serious penalties for it too. Ray Rice was suspended a season, and he got it turned around, all respect to him for realizing his mistake and making an effort to prevent future occurrences. All domestic violence charges against players should result in at least a one year suspension.
Domestic violence is a serious and heinous crime. No human being should be allowed to harm another human being. To exempt "sports players" from this axiomatic moral imperative would be an egregious step backward in the development of ethics and morals in the world. A person's status as a "celebrity" or "star" has no meaning in an issue of this nature.
Yes Greg Hardy should have been suspended and in fact players in ALL sports, at ALL levels should be subject to being suspended for acts of domestic violence. We should be sending a clear message that there no excuse for acts of domestic violence, in any context! We need to END THE VIOLENCE.