The Irish, Italians and Poles were never considered non-white. Distinctions were made between Anglo-Saxons or Nordic races and others - but it was never stated these were the only whites or Europeans AFAIK. The "ethnic whites" always ranked above Asians, for example and obviously had major advantages that Black Americans lacked.
By the turn of the 20th century, Irish were already seen as part of the northwest European mainstream group though, as southern and eastern European immigration increased. And after WWII the discrimination against white ethnics and Jews broke down.
Legally this was true in the sense that Irish, Italians, Poles, etc. could always become citizens, vote, hold public office, and couldn't be enslaved. Despite what your racist facebook uncle might tell you, "Irish slavery" wasn't a real thing, at least not in the New World, and the photos that he posts which supposedly "prove" this are just poor people, not slaves. However, "ethnic whites" weren't considered white
socially for quite some time. When this happened varied for different groups, but by the post-WWII era there was little perceived difference between different white ethnic groups.