People like to stereotype and label. But stereotypes and labels can be misleading. Let me give a practical example.
Stereotype: Charedim are anti-zionists and Religious Zionists are pro-zionist.
An interesting quirk of history: Rav Hutner decided towards the end of his life to move to Israel. He told his son-in-law and daughter "You're coming along". And they did!
RYB"S lived in Boston for most of his life until the end. When his son in law RA"L and daughter decided to move to Israel he was very, very upset. He wanted them to stay in the States. Understandably - He loved them and ostensibly saw his son in law as his successor. But if they live in Israel they are far away and his son-in-law can't succeed him. [It comes out that NOBODY succeeded him with no lack of respect to the great Rabbeim at YU. Just nobody can equal his greatness in Torah and impact on the community].
So the "Charedi anti-zionist" Gadol moves to Israel and takes his married children with him. The "Religious Zionist" Gadol stays in the US and laments the move of his children eastward to the Land of the Holy.
Note: This is not a criticism. I am not one to criticize Gedolim. I just try to learn from them and emulate them when possible. They were certainly both לשם שמים. Just a presentation of the facts.
Also - The Israeli branch of the Soloveitchik family has a Hashkafa about the Medina very close to Satmar. The American branch of the family are by and large strong Zionists [to the best of my knowledge].
Mussar Haskel: Don't be quick to label. People are more complex than trite labels.