Well, it's not a coincidence that the English word for the language of the Netherlands is the same the German state calls itself: "dutch" / "Deutsch".
A people and their language predated the concept of nation-states, but when the latter arrived obviously (geo-)political interests started to blur the facts.
So if you conflate the German state with Germans (I'd challenge that and view the German state as a continuation of the Prussian state), and you don't like the interests of the German state, it is predictable where you'll land on this issue.
Because of this, even if their national anthem does so, calling the Dutch Germans would infuriate them and rightly so, because it would imply justification to some for things like those happening between Russia and Ukraine right now.
I think in the end it is also a matter of "national" self-confidence. While Luxemburgish is virtually indistinguishable to the German ear from say the dialect of Cologne, Swiss-German is hardly understandable for anyone outside of Switzerland. Yet, the Swiss don't have an urge to re-label their dialect as a separate language. And the urge of the Dutch to re-lable themselves is lesser than that of Luxemburg because seemingly no one questions their identity.
Also noteworthy are the different terms for "German" in different languages, they're quite far apart: "Deutsch", "Allemagne", "Nemți", which all derive from the names of different Germanic tribes. Depending on which tribes surrounding countries (which were faster to establish nation states) were closest to, that's what they called all Germans. And it stuck.
true-ish. I'm not aware of any tribes that would give name to Deutsch and Nemti. Rather, Deutsch is the generic self-description for all tribes, and Nemti was a generic description of all tribes by slavic people (ie Niemy in polish meaining "without the ability to speak")
I thought:
Deutsch: https://en.m.wikipedia.org/wiki/Teutons
Nemți: https://en.m.wikipedia.org/wiki/Nemetes
But at least Deutsch does indeed appear to have other origins according to: https://en.m.wiktionary.org/wiki/deutsch
All national identities are to a large extent constructed (or less charitably: made up). So the 21st-century idea that Germans are people with a passport from the Federal Republic of Germany is not really any more or less valid than the 19th-century idea that Germans are a cultural group spanning various states including Austria (and maybe even including the Netherlands).
Edit: FYI, I've mentioned Luxemburg as a counter-example to Switzerland/Netherlands, because the state of Luxemburg attempts to have their German dialect officially recognized as a separate language…
I mean, they put umlauts on Es, that's got to count for something....