This badge from my alma mater has no such drunken Paddy look.
Er, yes it does, look at it, it shows the usual squat, low-browed, simian-faced, hairy Irishman in pug hat and coat tails squaring up to brawl with someone.
Examine the anti-Irish cartoons and propaganda in 19th century pamphlets and publications in England and the US and this is the brutish, ape-like characterization you will find. It is exactly comparable with anti-semitic characterization of the jowly, long-nosed Jewish moneylender from the same time.
If Notre Dame wishes to keep it, that is their business and no concern of mine, but at least you should know the disreputable origins of the image.
Cheers
irish guard