Jews, If someone mistakenly calls someone the Messiah...?

would that person still be a Jew? Like some of the followers of the Lubavicher Rebbe, for example? Or even Jesus? In the later case I would be refering to someone who only claimed him as the Messiah, but not a God and continued to live exactly as he had before accepting this person as Messiah? This has happened before in history, so how did the rest of the Jewish community react in these cases, and what is the view theologically? Please, I'm not only looking for the view on Jesus only, but more specifically,in the other cases as well.