There have always been problems, the question is just whether we can respectfully disagree or if one side feels the need to enforce their shittas as the only correct path.
Tell me, how are we not respectfully disagreeing? The most disrespectful thing we said is that we think everyone should learn Chassidus (not necessarily Chabad)? How much more disrespectful is this compared to Reb Yisroel Salanter’s campaing to bring Mussar to the Yeshiva world (which was controversial in its day (“Mussar is a medicine” vd”l)).
Can this be compared to the literal nonsense that people made up about Chabad? You know, like Tomchei Tmimim learns Tanya or Likkutei Sichos all day (Jokes on them. There is no Seder to learn either. Both are learned outside Seder. We literally don’t learn the Rebbe’s works during Seder. Even the Chassidus that we learn, is 90% of the time the 5th Lubavitcher Rebbe’s Maamorim. And that’s 3 hours a day. The rest of the time – the same Gemara/Rishonim and Shulchan Aruch you do. OK. We learn Shulchan Aruch HaRav since we do Paskin like him, but on Simanim where we don’t have Shulchan Aruch HaRav, like Hilchos Chanuka, we do learn Mishna Brura.) or how Lubavitch is all Frei (answered a few posts before), or how Lubavitch does Mivtzoyim all day (again, we only do Mivtzoim Friday afternoon when all Yeshivas don’t have Seder anyways). Forget about all the claims that every story said by Lubavitchers was maliciously invented to put down the Yeshivish velt (also Lo Haya VeLo Nivra, and also answered above). Is this called “respectfully disagreeing”?
Listen, Reb Moshe respectfully disagreed with the Rebbe. Many times. And publicly, it’s all printed in Igros Moshe. But if you’ll notice, we have no Taynas on him. Lubavitchers sent him Shaalos. Because he was actually respectful about the disagreement. Kach Darkah Shel Torah.