Even if we,’d agree to consider both parties Gedolei Yisrael, when there was a fight between Rav Yehonasan Eibishitz and Rav Yaakov Emden, “A majority of the Rabbanim in Europe publicly expressed support for Rav Eibishitz in letters that they wrote to him, and in many of the cities excommunications were announced against all who support the machlokes or who maintain in their homes literature which defames Rav Eibishitz. Rav Eibishitz even sent copies of his amulets to many respected kabbalists (including Rav Eliyahu of Vilna), who all confirmed that the content of the amulets is kabbalistically comprehensible and there is no basis for the interpretations of those who are against Rav Eibishitz” (Rav Yonasan Eibishitz, Hebrew Wikipedia).
There is a right and wrong. There is a mitzvah d’oraissa to be moicheh when wrong is taking place. The fact that people will be offended etc. is irrelevant. This isn’t the avaira of supporting machlokes. To the contrary, it is the mitzvah of tochacha.