R’ Chaim Vital wrote in the introduction to Etz Chaim that the oaths only lasted for 1,000 years. That time is long past, so they’re not in effect anymore.
R’ Meir Simcha, in a letter to the Keren Hayesod, said that the oaths are only aggada, and even if they were halachically binding, the Balfour Declaration removed any issues.
R’ Shlomo Kluger held that since the other nations persecuted the Jews unjustly, the oaths on the Jewish nation are removed. He quoted the Shulchan Aruch that says that if 2 people take an oath and one breaks it, the other one is not obligated in it any more.
So there you have the 3 opinions that the oaths aren’t in effect anymore, and therefore Zionism doesn’t break them.