Earlier quoted context omitted.
Sparta, their entire civilization basically atrophied because of it.
Sparta and Rome suffered from the same problem, actually. They approached it differently. Rome survived. Sparta didn't. The problem was that citizenship or social class was based on inheritance and it was essentially a closed system. At a time when infant mortality was so high and being in the military was risky, this meant that the ruling class diminished over time. The author of this piece touches on how most soldi…
To be a bit pedantic, you're combining two different senses of 'white' there: in the US, being culturally considered white by others was distinct from being legally considered white by the government, because from the Naturalization Act of 1790 onward, naturalization was legally limited to "free white persons" (subject to some later modifications, though "free white person" remained a category). From a legal perspective, the Irish (and Germans) were always considered white, and there was never any question (if I recall correctly, for Mexicans, there was at some time advice that legal whiteness should actually be determined based directly on skin color). From a cultural perspective, views could of course be more varied, and there's the complexity that views and discrimination could certainly be based on factors other than seeing people as white or non-white, even at a racial level for the types of people who made distinctions within whiteness. And of course, cultural views remain varied: I've been around some very waspy wasps in the US who, knowing my Greek name, probably didn't consider me to be entirely white.
By the time of the case you cite, the legal question more broadly had become a mess of different and sometimes contradictory decisions, in part because, when it actually needed to be litigated, 'scientific racism' and 'common knowledge' could go in very different directions, as one might expect from something so arbitrary and contrived. Dow was decided on scientific racism lines, and made some Arabs white (particularly Syrians), though there were later cases with the opposite determination, in part because Dow was just Fourth Circuit, but also at times including arguments like 'from a place not bordering the Mediterranean'. Thind, on the other hand, was determined on common knowledge lines, and can bizarrely be summarized as 'being Aryan and very racist does not make a person white' (the entire set of pre-Thind cases around Indians, actually, often have wild and arbitrary decisions; I recall that one lower court decision could be summarized as 'this scientific argument seems dubious, but the guy seems like an upstanding character, so it seems fair to say he's white').