mdd: Litvishe Gedolim object to a number of the shittos of other Litvishe Gedolim — and Chasidishe Gedolim object to a number of the shittos of other Chasidishe Gedolim. It’s been like that for over 2,000 years. And it’s normal and acceptable and it’s all Torah.
Nevertheless, the Litvish Gedolim sit with the Chasidishe Gedolim on the Moetzes Gedolei HaTorah as well as on many other inter Litvish-Chasidish functions. (Agudas Yisroel, Siyum HaShas, Yeshivos, etc.)
They each fully accept each other as Gedolei HaTorah. Need I quote for you the hespedim they gave for each other (i.e. The Satmar Rebbe’s amazing hesped of Rav Ahron Kotler at his levaya; or the hespedim by Rav Yitzchok Hutner and Rav Yaakov Kaminetzky of the Satmar Rebbe; and many others.)