Hasidic Jews are orthodox, but not all orthodox Jews are Hasidic. And orthodox Jewish views on Israel vary pretty widely, so the statement that forms the premise of your question, that Hasidic Jews do not recognize Israel, is an overgeneralization.
Now, the most widely known fringe group of anti-Zionist Jews, Neturei Karta, is made up of Satmarer Hasidim. It's actually a really tiny group, comprised of a minuscule percentage of the Satmarers themselves, who in turn, are one of hundreds if not thousands of Hasidic sects, who in turn form but one branch of orthodoxy Jewry, who in turn are a minority among Jews in general. But they get a lot of press because they're the ones going to Holocaust denial conferences and smooching with Jew-hating despots for the cameras.
One reason many orthodox Jews are not content with the State of Israel as it is (and this does not necessarily constitute non-recognition any more than having a beef with the U.S. government over one or more of its policies means not recognizing the sovereignty of the United States), is because it is not a Torah-based state. Israel is a state created by Jews, for Jews. But its status as a Jewish state is tenuous at best.
In traditional Jewish belief, the return of Jewish sovereignty to the historic land of Israel is part and parcel of humanity's redemption, and the coming of the long-awaited Messiah. But Jewish sovereignty is supposed to be under the ultimate kingship of G-d. Which means that it should be run according to G-d's law, the Torah. Also, there are different opinions as to when the Jewish state is supposed to come into existence. Some hold that the arrival of the Messiah is a prerequisite for this, and as such, we Jews are wrongfully trying to force G-d's hand, as it were, by creating the state before the Messiah shows up.
Even the suicidally anti-Zionist orthodox Jews (I say suicidally because these are people who embrace people who would want them dead for the crime of being Jewish except that THEY serve the anti-Semite's propaganda purposes -- there are reports that show Neturei Karta to have been on the payroll of the PLO, at least in Arafat's time), even they support the existence of a Jewish state. They simply want it to be a Torah-based state, after the Messiah's arrival. Anything else, in their view, is an affront to the Creator.
For most of the rest of us (orthodox Jews), the Jewish state has its flaws, some kinks to be ironed out, but its existence, despite these flaws, is nothing short of miraculous. We see it as a step in the right direction, and, for the religious Zionists (orthodox Jews for whom Zionism constitutes a core part of their ideology - religious Zionism is like classical secular Zionism only with its roots in Torah, and without all the socialist nonsense), the re-creation of a Jewish state indeed represents the "first flowering of our redemption".
I hope you find this information helpful.