Rav shach would consult rav moshe frequently on political issues; it’s not only that the Lubavitcher rebbe was in Brooklyn. Rav Moshe was in Manhattan, which is a few miles further from eretz yisroel.
Those who hold of being involved in the government believe in trying to make it as close to judaism as possible, not a separation of church and state. Even rabbi yoshe ber soloveitchik said that a state that will not become religious isn’t worthwhile. The Lubavitcher rebbe presumably would want the state to be run according to halacha too. Whether that makes us “no better than Uganda” is not a logical, Torah based argument.