The Lubavitcher Rebbe was quoted in one of his biographies as saying that he was not opposed in general to people making aliyah, and in some cases had encouraged Jews to do so.
However, generally he discouraged rabbis and other leaders from making aliyah if their services were needed in the local community in galus. The reasoning was that one should put the spiritual needs of others before one’s own.
As far as his political positions were concerned, he was 100% against any territorial concessions, because they would threaten Israel’s security. So he agrees with the far-right Zionists but not for “Zionist” reasons. The only party in Israel that conforms with that view is Bayit HaYehudi. However, at some point he told poeple to vote for the most charedi party. So I imagine some current Chabadiks vote for Bayit HaYehudi while others would vote UTJ or Shas.