Violence in response to racism can be justified when a person or group perpetuating racism uses violence. Those who have suffered violence due to racism in the form of police brutality, lynchings, or hate crimes have dealt with both physical and emotional pain on the basis of race. If someone reacts violently after being a victim of violence due to racism, it is justified because the racist person instigated it.
Yes, violence is appropriate in some circumstances. Racism is one of the circumstances in which violence is appropriate due to the level of hurtfulness of racism. Causing physical pain is an appropriate response to some forms of emotional pain. This is the only way to get even for some things.
Yes, vigilante violence for whatever reason should not be tolerated. Professional athletes, whether they want to be or not, are role models. As such, there has to be repercussions for inappropriate behavior, regardless of how well-meaning it was. The inappropriate behavior of one person does not excuse inappropriate behavior of another, and this should be especially true of professional athletes. Furthermore, professional leagues should not pick and choose which cases of assault they will punish. It would be inconsistent to punish one athlete for engaging in a brawl after his mother was insulted and not another because a racial slur was dropped.
Racism is not a crime. While it is highly negative and clearly not a good thing, it is not something that warrants fighting necessarily. Racism can not really be prosecuted and if you start the fight you are the one liable for prosecution. However I do think that in specific circumstances violence is necessary, but in the current state of the US I think it to be highly illogical as racial divide is just being exacerbated and violence done without much true reason.
While it is admirable for anybody to stand up for somebody being subjected to something as vile as racism, when you choose violence, you are sinking to the lowest common denominator. Somebody in that situation has to be the mature, thoughtful adult and control the situation. It sure as heck won't be the drunk racists.