Regarding the OP:
The Religious Zionists have staked their future and indeed their faith with the Zionists. They have created a new nationalist religion called “Religious Zionism” that happens to contain many Torah-based practices in addition to Nationalism/Zionism and many severe distortions of the Torah, CH”V.
There is also the minor matter that the “Religious Zionists” have acted against the Torah and Klal Yisrael going back to, for example, Yaldei Tehran, pre-1948. The Brisker Rav lived in E”Y both before and after the Zionists formalized their invasion of E”Y with the creation of their idolatrous State. The Brisker Rav wrote regarding the “DL” education system that they preach a drop of Torah mixed in to a sea of heresy.
Viewed in this light, it is understandable why the traditional orthodox population in E”Y is not exactly thrilled with “D”L.
This cannot be remotely compared to Chassidim and Litvaks and also cannot be compared to Traditional Orthodox and “MO” in the USA.
Regarding the latter, Rav Shimon Schwab, years ago, implored MO to abandon their “stagnation” and “foolishness bordering on heresy” and return to the true path of the Torah. B”H, it seems that, at least in part, this is happening. Countless former YU students go on to study in Traditional Orthodox yeshivos both in Eretz Yisrael and in America, etc. B”H.