The hashfafic separation between “chareidim” and DL/MO is far more vast than the hashkafic separation between the Litvish and the Chasidim. Whereas the Litvish and Chasidim have fully accepted each other as eilu v’eilu, neither of them have accepted the DL or MO hashkafas as eilu v’eilu.
You can search the threads here for fierce discussions why the above point is the case, but the reality is that it is the case. Not every shitta is accepted as an eilu v’eilu. And the chareidi world doesn’t accept their view (mostly on zionism and gender issues) as acceptable under the Torah.