Sorry, but if you asked any meshichist if they would accept R' Shach as moshiach if he were chosen they would all say yes in a heartbeat. Sure they may want to clarify things with Eliyahu, but that wouldn't hinder them.
Thus nobody truly believes that the Rebbe and only the Rebbe can be moshiach. And refusing to daven in such a person's shul or eating their food just because of that belief is more foolish IMHO than believing that a holy and learned person to be a strong candidate of being moshiach. There is nothing halachikly wrong with that belief.
And I hope you don't drink any Bartenura wine btw
