I hope this helps clear up the confusion.
Over 10,000 Orthodox Jews protesting the existence of the state of Israel, and the recent beating of Orthodox Jews who protested in Israel against the uprooting of Jewish cemeteries of antiquity which was done in order to enable the construction of a highway #6, near Haifa, Israel – protest in front of the Israeli consulate New York City, Thursday, April 28, 2005
10,000 Demonstrate in NYC Against Israel on April 28, 2005
They are Satmar sect of Hasidim , not the same a Lubavitcher anyone who is Jewish should know this, reading the op it reads like a generic orthodox , thus implying orthodox rejects Zionism
Hasidic groups largely emigrated to the US after the Holocaust. Each sect follows a single grand Rebbe, admiring him to such a degree that his table leftovers are considered blessed. The grand Rebbe position is generally hereditary, although it may pass to a son-in-law (who may have been selected for this) rather than to a son. I can think of two current Hasidic groups that have opted not to replace a beloved Rebbe after he died, and who are thus without a single leader: Breslov, who have been rebbe-less for 200 years, and Chabad (see below.) Aside from Chabad, they are very inward-focused, with the entire sect generally living in either one place, or a short list of communities (e.g. Belzers live in Jerusalem, Borough Park, Brooklyn, and I think Montreal.) The lingua franca is generally Yidish; boys, whose Jewish education is prioritized, may receive very little English education and may speak English poorly and with a heavy accent, even if their family has lived in the US for 4-5 generations. The sexes are even more rigidly separated in non-Chabad Hasidic groups than in other UO groups; for example, wedding celebrations are generally held in two separate rooms, rather than in one large room with a divider. The men tend to have distinctive dress, in the style of Eastern European gentry of the eighteenth and nineteenth centuries, and I find that when people think of "Orthodox Jew," they tend to be picturing "Hasidic man." Some groups get along quite well (e.g. they may marry across sect lines), and some really don't. I'm not plugged in at all to the intricate world of Hasidic politics, and can't really give you a good overview, but it can get fairly ugly, especially in Israel. This tends to be political/financial rather than purely religious, although they may have slightly different interpretations of halacha (and yes, the narcissism of small differences definitely applies here.)
Chabad is a Hasidic group, one currently riven by a division between those who revere the most recent Rebbe, but acknowledge his death in 1994, and those who still consider him the Messiah. (Frankly, non-Chabad Orthodox Jews find the latter group quite disturbing.) The most recent Rebbe charged his followers with bringing all Jews closer to observance of Jewish law and Judaism. These are the Hasidic Jews who may have asked you if you were Jewish at some point. They do not proselytize outside of Judaism, but can be quite aggressive within it. To that goal, they've founded centers around the world, and may live far from any established Orthodox community at all. They obviously choose to interact with many outside of their own groups, are more MO in terms of gender segregation, and are big fans of the internet and technology, which allows them greater outreach. Other Hasidic groups tend to be uncomfortable with them, and they don't have much social mixing between the two.
Haredim and Zionism - Wikipedia
Groups which do not recognize Israel

Flyer in
Meah Shearimwhich declares "No entry to Zionists!"
There are a number Haredi groups which not only oppose Zionism, but also do not recognize the State of Israel. Among them are the Hasidic sects of
Shomer Emunim (and its offshoots,
Toldos Aharon, and
Toldos Avrohom Yitzchok),
Mishkenos HoRoim, and
Dushinsky. In July 1947, Rabbi
Yosef Tzvi Dushinsky, Chief Rabbi of the Jerusalem-based
Edah HaChareidis, declared to the
United Nations his "definite opposition to a Jewish state in any part of Palestine". The largest anti-Zionist Hasidic group is
Satmar, which has around 130,000 adherents worldwide. The group’s position was crystallized by their charismatic leader, Rabbi
Joel Teitelbaum, who authored comprehensive and polemic tracts detailing his opposition to Zionism. He encouraged his followers who lived in the "Holy Land" to form self-sufficient communities, rejecting social state benefits, and not to vote in general elections. Anxious not to be viewed as supportive of the actions of the secular Israeli government, which he viewed as an abomination, he instructed people not to visit the Western Wall and other holy sites which had been captured by Israel in the 1967 war. One of the most extreme sects is the
Neturei Karta. Formed in 1938 as a breakaway from Agudath Israel, its 5,000 members are based mainly in
Jerusalem and
Beit Shemesh. A faction within the group openly supports the
PLO and
Hamas, and calls for the "peaceful dismantling of the Zionist entity".
Groups opposing secular Zionism, but recognizing Israel
The
Agudat Israel is an international organization (with an Israeli association) of various Haredi groups, mainly from the Lithuanian yeshiva communities and Hasidic groups such as
Ger and
Belz. It initially adopted a stance of disregard for the State of Israel, motivated by pragmatism. They attempted to influence the politics of the State of Israel from within, by participating in national elections and sending their representatives to the Israeli Knesset, but still did not take full part in it by not serving in its military, and not celebrating any of the State's official holidays. Today, the organization has shifted over time to somewhat supportive of the state, although not officially recognizing itself as a pro-Zionist party. An example of this is the revolutionary Hesder legions in the IDF, which is a unit that combines religious studies and national service, designed specially for Haredi Jews. The Agudat Israel party in the Knesset is represented as
United Torah Judaism, a collective party of Agudat Israel and Degel HaTorah. It tries to influence the Knesset with a pro-Judaism outlook, by mainly focusing on funding for Jewish education (
yeshivas), exemption from military service for Haredi yeshiva students, and trying to strengthen Israel's Jewish identity.