sechel> all the gedolim supported the rebbe and held of his as the gadal hador and many held he was moshiach
At minimum, I think LR, R Moshe and Rav YB Soloveichik had respectful relationships between each other. Maybe, as I once was told by a Rav about another Rav with whom I suggested a cooperation: “at least we learned not to hurt each other’s work”.