This explanation seems a little less problematic (as it’s based less on the stereotype of Irish people always being pissed):
“Early versions of the term Irish Exit come from Irish Americans leaving social functions like Church, football games, and plays. When the functions let out people would congregate outside and chat with each person they knew and say goodbye before heading home. This usually added 30 minutes to an hour to the evening. When there was little or no time to do the customary goodbye, the family would leave through the side door. The side door move became known as the Irish Exit. The term has come to mean leaving a place without saying goodbye to those you are with or those you came with.”
I get what you mean, though.