I guess because most other groups don't get in a tizzy when they see FIGHTING IRISH, or Boston CELTICS, etc, etc.
As you alluded, Notre Dame has as its mascot a drunken, brawling Irishman. Fine for an Irishman to be portrayed as a drunk, but no firewater references to American Indians, please.
It's OK to refer to someone welshing on a bet, but don't dare accuse anyone of being an "Indian giver."
It's perfectly acceptable to refer to the legendary penny-pinching of a Scotsman, but you must not ever imply that a Jew bargains a bit too hard.
And all bets are off when Southern or Appalachian white people are referred to, even on network TV. Can you imagine the outcry that would have ensued if the feckless bumpkins in the Beverly Hillbillies had been black or Latino?