Generally speaking Irish immigration took place quite a bit earlier (early-mid 19th century) than Italian immigration (late 19th century to early 20th century), so the Irish probably resented sharing the neighborhoods with southern Europeans while they themselves were still trying to break into the WASPy mainstream of American society. Seems silly to us now, but even being Catholic meant you were not a "real American" for a very long time in this country; the Anglo-Saxons dominated the power structure for generations.