I *think* the purpose is to say "I'm just as ethnic as you!", entirely ignoring the point that nobody has seriously discriminated against Americans of German heritage since the Second World War, and that overt discrimination against Irish-heritage Americans ended earlier. "No dogs or Irish need apply" is, rightly, a bitter memory, but has nothing to do with the condition of modern Irish-heritage Americans who are, if anything, considered vaguely cool. (See: the bizarre American fixation on St. Patrick's Day.)