I don’t know why this point hasn’t been brought out, but in most incidences when the Zionist try to institute decrees (they call them laws) that are in opposition to our (Chareidi) Torah values the DL tend to side with them instead of us. That kind of makes it difficult for us to live in harmony with them.
The Litvish and Chassidim at times disagree with how to deal with the Zionist, but regardless we sit on the same side of the fence.