I'm not sure why saying your background includes "Jew" is bad. Or are you saying it's bad to have Jewish ancestry?  "Dirty Irish" is used as a reminder that the Irish were considered the low lifes at they time many immigrated to America.  The chuckle is that now they are non-controversial and mainstream compared to the rest on her list. 

It sure looses a lot when you have to explain.  Geez Barry, try to figure it out on your own next time.