Yet, there definitely seems to be a 'look' to Irish design as well. Are we being stereotypical or is there something behind that?
Irish typography has a very specific history. There was actually a family of Gaelic typefaces designed during the 16th to 20th centuries for use in Ireland. The forms were derived from calligraphic handwriting and include the insular forms of the Irish alphabet. This can include all twenty-six letters of the Roman alphabet, the letters with accents and the consonants with a dot above them.
This is most likely why there are certain typefaces that just scream Irish, because they were made to do that. Today, these typefaces are generally only used for design purposes, such as on pub signs, posters, greeting cards and headlines on traditional newspapers.