the Disagreement between Rav Shach and the Lubavitcher Rebbe

"So if Rav Shach, let’s say, and the Lubavitcher Rebbe may have sichsuchim, some arguments; I don’t know if they have, but if they have some sichsuchim, it’s none of our business. It’s the fire of Gehenim to open up your mouth. Keep your mouth closed. It’s a tragic mistake to mix in.
And the wisest way is to say nothing at all, and to have the greatest derech eretz the greatest respect, for all those people who are recognized. After all, the Lubavitcher Rebbi is recognized by many people. And Rav Shach is recognized by many people. So we should keep our mouths closed and recognize both of them. That’s the way we should follow."
All Credit is to Toras Avigdor.org

“When Rav Shach and Lubavitch had differences, I came home, eager to hear my father’s take. He was a real baal hashkafah, and I was sure he would have insight into the disagreement, but when I asked him, he looked at me in astonishment. ‘What’s your last name, Itche Meir?’ he asked me, repeating the question a few times. I had no idea what he meant. Finally, he explained, ‘Is your last name Shach?’ he asked me, ‘or is it maybe Schneerson? How exactly does this machlokes pertain to you?”
All Credit is to Mishpacha.com