> Can you list some important implications of "is Pluto a planet or not?"
I remember reading in 'A Short History of Nearly Everything' that Pluto was the first and only planet discovered in the USA, all the rest having been discovered in Europe.
I don't know if that had any implications for the reactions to IAU decision to demote Pluto to a dwarf planet, but it's easy to imagine how it would have been an even bigger deal if the other planets had been discovered by, for eg., Russia back in the day.
Is Pluto a planet? No. Although various people have strong feelings about implications in education and elsewhere--in both directions.
Languages and dialects can with respect to policies like bilingual education. If it's just a dialect, then you may argue there's no need to treat native-speakers differently. If there's a genuinely different language then you may or may not decide that bilingual education is necessary but it tends to be a different discussion than in the first case.
Also language preservation - and there's a direct analogy to preservation of species. When we consider something a separate species, there's that much more impetus to preserve it from extinction, for the sake of maintaining diversity. Similarly, when we consider something a distinct language, there's similar impetus to preserve it. Dialects (usually) aren't extended the same deference, and are left to live and die on their own.
I'll leave Pluto to others but whether something is a language or not has tremendous political significance, which is obvious to anyone who's spent any time reading about China.
It doesn't, really. Chinese policy is to make sure everyone speaks Mandarin, to promote in-country unity. The rhetoric they employ to push that goal is independent of the goal; there is no question anywhere that English is not a dialect of any Sinitic language, but English was required in Chinese schools for policy reasons and they are now beginning to phase it out for (different) policy reasons.
There are no policy implications to using a different term for Cantonese (though the relevant Mandarin terms are 方言 "the speech (语言) of a place (地方)", which makes no distinction between "dialect" and "language" (though "linguistics" is 语言学, the study of 语言), and 粤语 "Cantonese", which is a term fully parallel to 英语 "English", 法语 "French", 日语 "Japanese", etc.). Regardless of term, the policy will be that schooling takes place in Mandarin.
No, that's not really true; the PRC's position is predicated on the claim that Mandarin is a degenerate dialect of Cantonese, and not a language in its own right. They also believe, rightly or wrongly, that acknowledging the multiple Sinitic languages would threaten their status as one cohesive nation. It's also rather disingenuous to take the two component characters of 方言 apart to argue it means something different than it does; telling me it means "direction-speak" is no more illuminating than telling me "telephone" means "distant voice."