It was precisely rabbi kook’s grafting of nationalism on to Judaism that was his major, overarching issue. The shevuos are an issue too, but disagreeing about their applicability is an area which one can argue in halacha(erroneously, according to the vast majority, more on that later) and still be completely within the mainstream of halachik judaism.
Nationalism means that a nation is defined and distinct based on characteristics like a shared language, land, culture, and ethos.
Judaism always believed that being a jew is defined by following the Torah. The din of yisroel is passed down by mothers, but it can also be acquired by conversion. Thia, rav elchonon writes, js the greatest refutation of zionism. Secular zionism believes in redefining the jew from a religious construct, created in the midbar (hayom hazeh nihiyaysi l’am, today you are a nation to me – by matan Torah, not in eretz yisroel), to a nationalistic one, a person defined by shared lineage, land, history and language.
Religious zionism said that one is a jew because of (insert italics) both things. This is precisely why rav elchonon said “zionism is avodah zara, and religious zionism is religion mixed with avodah zara”
Rabbi kook was the architect behind this ideology.
The shevuos are a different issue; the taanos you mentioned (and fhere are others) are invalid for a few reasons:
Consent of nations: this is a machlokes in concept, and the maharal holds it isn’t valid. According to those who hold it is valid, including thw avnei nezer, the Balfour declaration was not agreed upon (insert italics) by the people who lived in eretz yisroel, and their suroundings, hence the war that started the day of the declaration of independence. England also reneged from this agreement as a result of widespread terrorism on the part of the Zionists and intense pressure from the Arabs. They were mesalek themselves from the whole issue, letting the Zionists hash it out with the Arabs, and that they did.
The question of the oaths being mutually violated is a bit more nuanced. There is one opinion which says this, but it’s not mentioned by the rishonim and achronim, such as the ramban, rambam, rashbash, piskei riaz, maharal, etc. Even according to that one shitoh, which goyim violated their oath? Germany and a few other European nations. The grand mufti supported Hitler(largely because of animum to zionism!) But did not kill or even expel any jews, and neither did the arabs living there, nor did the British, who were fighting Hitler and his killing machine.
So why should one nations violation of their oaths invalidate ours to others?