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.
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.
Historically it was, back when immigration from parts of the world south of the Sahara and east of the Dasht e-Lut + Urals was legally restricted. Doesn't make much sense to frame the emerging majority "mainstream" culture/in-group as "white" now that those restrictions are no longer in place, and there has been more geographic and cultural diversity among newer immigrant waves.
I'm skeptical that intermarriage will lessen the social separateness of certain non-white groups such as Latinos and Asians (whether Subcontinental or otherwise) to the extent that Bismarck is suggesting. Nor do I see any reason to believe that they or the fraction of their descendants who are mixed race will be considered
more "culturally mainstream" than the ADOS community is today.
That being said- lingering social separateness doesn't have the electoral implications certain people here might think it does.