I suppose the argument is that anyone who might serve as a role model for young people has to abide by a higher moral standard than everyone else. If he or she misbehaves and is tolerated by their employer, that might suggest to those who admire them that such behavior is acceptable. That might encourage others to indulge in it. Provided these rules are made clear to all sides I cannot see that any great injustice results.
Read another response by Oliver Leaman
Recently, the NFL has become embroiled in high profile cases of domestic violence by its players (most notably, Ray Rice and Adrian Peterson). Many critics demand that the league suspend or otherwise discipline the guilty parties. But why, in general, should an employer be expected to address bad actions by its employees when those actions fall outside the scope of work-related duties? What business is it of my employer's whether I commit crimes when I leave work?