It doesn’t seem any of the hassidic sects accepted Zionism, and even today none of them view the establishment of the State of Israel as the fulfillment of a mitzvah. The Hassidim do not have prayers in their siddurim for the well being of the State of Israel and they don’t regard it as "resheit smichat galuateni." Additionally, Hassidic culture is very much a diaspora culture with the emphasis on Yiddish and the donning of Eastern European garb. Why are Religious Zionists encouraged to learn Hassidut?
As is often the case, there is a world of difference between ideology and the implementation of that ideology. As the saying goes: “Judaism is perfect, Jews are not”. Just as people often join a political or youth movement for the sake of the ideology, but in the end, the “party”, club or sect unfortunately turns from a means into the goal itself (like what happened to communism), so too one must differentiate between the ideology (!) of chassidism and the particular sects of chassidim. Their ideology is firmly based upon biblical and rabbinic literature and classic kabbalistic sources, and accordingly are very Zionist, but in practicality, over time, each sect pulls in a different direction, usually having very little to do with ideology (not only on this ussue…). Accordingly, to get the authentic and complete “version”, one would be wise to learn the original biblical, rabbinic, kabbalistic and Chassidic sources which are overflowing with love for the Land of Israel, the Nation of Israel, the Hebrew language and redemption, and a clear tolerance even for the secular Jews and the physical world which are generally secular and mundane (that side of life with which nations, including the State of Israel, are preoccupied). Chassidic ideology even takes it a step higher, stressing to reveal the G-dliness in these fields, as well. In short, all of the above is exactly religious-Zionism (as stressed throughout the writings of Rav Kook, often based upon davka kabbalistic and Chassidic sources!), but the “political” affiliation unfortunately blinds most Chassidim. The Radziner stream (especially the previous Husiatiner and Sadigora Rebbes) is a famous exception who actually celebrated Israeli Independence Day, but their followers “chose” not to follow their rebbe on these issues, thus “toeing the charedi party-line”. Even their successor sons dared to disagree (!) with their fathers on this issue. This just proves the point that “it’s hard to take the Jew out of exile, but it’s even harder to take the exile out of the Jew.” That doesn’t mean that religious-Zionism, which is much closer to the original Tanachic (Biblical), rabbinic and Chassidic ideologies, should make the same mistake as the Chassidic sects, and that's why we do suggest to learn chassidut. Just as any objective reading of the Bible shows that the ideal Jew (like Moses, Joshua, and David), who studies as much Torah as possible, also serves in the Jewish army. Here too, most charedim “bend over backwards” to “toe the charedi party-line”, not only twisting logic but even ignoring and defying (!) all (!) of the sources, by not serving in the Israeli army. As you hinted, their ideology fearing change yearns to maintain the culture of diaspora, and unfortunately overcomes their Jewish and Chassidic ideology. In short, if you want truth, it’s wiser to study and go by the eternal and objective sources and not by the political alliances, or the agenda of the Artscroll (or any other) translator. On the one hand, ba'alei tshuva have a huge advantage of objectivity, on the other hand their lack of Hebrew "locks them" into use of the subjective translations. In addition, those new-comers to observance often harbor an inferiority complex, feeling that they “must not be understanding the sources properly” if their local rabbi or chassidic leader teaches otherwise. I hope you succeed in overcoming these valid but unfortunate obstacles to objectivity. If there was no other alternative, we’d be in trouble, but this is exactly the beauty of the “option” of Torah-true religious-Zionism (which is the majority of orthodox Jewry, though living in America, one may not realize that). It’s the opposite of reform- it’s leaving the exile to go forward to the past- to the original. With Love of Israel, Rabbi Ari Shvat