As Avi K mentioned, the “3 Oaths” are not brought down l’halacha in the Shulchan Aruch, the Tur, the Mishna Torah, the BaHaG, or any other codification of halacha.
Are they cited in any major Shailos V’Teshuvos of the Rishonim or the Acharonim prior to the 20th Century? I know they are discussed in the Rambam’s Iggeres Teiman.
In any case, as explained above, the issue of which Gedolim are greater, or even which opinion is that of the majority, is only relevant if you do not have your own Rebbi who you follow. So followers of Rav Kook or Rav Soloveitchik are not doing anything wrong, and in fact are doing what they are required to do, in following the teachings of their Rabbeim on Zionism.