I don't think Notre Dame is a valid comparison. The idea of Irish people as fighters has served as both a positive and negative stereotype throughout history.
I have to disagree somewhat. You are right that it can be viewed as a positive because it is a point of pride for some Irish. But if you were to look at it from a social justice standpoint the fighting becomes the main feature of the Irish community. It becomes the first and only impression an uneducated or ignorant person makes about that particular social group. Fighting can be perceived in a number of different ways. Perhaps it's simply a reference to boxing. However, to someone who is horribly PC, they might view the fighting stereotype to be a result of the drinking stereotype. We are all aware of the stereotype that says all Irish people are heavy drinkers (and in some cases have tempers as a result). I think if Irish people were black, more people would be up in arms about the label "Fighting Irish" because they would associate the two stereotypes and in that case, that would put a poor image on Irish people and as a result; hold them back from social resources or power. Being viewed as an angry drunk with a short temper paints someone as uneducated, uncivilized and possibly even primitive person. I guess that's what I was driving at.