I’ve just read an interesting article on what you might call “other Jewish Messiahs”. I wouldn’t argue with the conclusion that Bar Kochba probably did the most damage to Judaism of all of the 50 or so candidates.
However, I think the article misses the point of why modern Judaism considers Jesus to have been the most damaging. That’s because the result was a major rift in Judaism which produced a new religion which was considered non-Jewish, or at least it was following a rather painful process of separation which is dealt with in a very compelling way by Daniel Boyarin in “Border Lines” and in “A Radical Jew”. There are strong hints of the early stages of that process in Paul’s letters and in the book of Acts, but the process probably didn’t become complete until well after that, probably around the middle of the second century, much aided by Justin Martyr seeking to clarify an identity for Christianity as against Judaism.
How many ethnic Jews actually ended up following the new religion of Christianity is a hotly disputed subject; the standard Orthodox Jewish response would be that vanishingly small numbers of Jews, if any, would have accepted the Pauline disintegration of ethnic distinctives, those things which actually made Jews a people. There is probably now no way of establishing what the truth of the situation actually is; the New Testament witness would argue that significant numbers joined the new movement (I don’t say “converted”, because at the time I don’t think most would think there was a need to “convert”, seeing Christianity as a natural development within Judaism), but is clearly susceptible to allegations of bias. Rome too, it seems, had difficulty distinguishing the two, considering the very early reports of the Jews agitating at the instance of someone called “Chrestus” (Suetonius, writing probably around 100CE).
However, if one can assume that there were indeed significant numbers who joined the new movement (and, of course, all the very early members were Jewish), the fact that a new religion (and one with massive staying power) was thereby started would, I think, rank Jesus as the greatest threat. One has to recall that, for many Orthodox Jews, conversion to any religion other than Christianity is a failing, but becoming a Christian makes someone dead to Judaism (and funeral rites are not infrequently performed in absentia); conversion is thus seen as a form of genocide. Boyarin thinks, and I agree, that this attitude is a part of the increasingly acrimonious split which on the Christian side became antisemitism; I cannot now think that had it been Judaism which had achieved ascendancy there would not have been a major possibility of similar treatment of Christians, given the recent history of a resurgent nationalist Israel.
This thinking, however, leads me to posit a different ranking, based on which messiah figures came closest to instituting a new religion. Sabbatai Zvi has third place after Jesus there; there were at one point a very large number of followers and commentators at the time were concerned about the possibility of that becoming a majority in Judaism. However, the Sabbatarians proved not to have staying power, particularly after the forced conversion of their leader to Islam.
Second place, however, has to go to Menachem Mendel Schneerson, who is perhaps politically skated over by the article (though, to be fair, he cannot be blamed for many, if any deaths). He was the last Lubavitch Rebbe (and earlier Lubavitch Rebbes had also been hailed as messiah to a lesser extent). His followers are extant as Chabad Lubavitch, who have a very prominent presence in conservative Judaism to this day (running many Jewish educational establishments inter alia), and having a substantial proportion of people who still hold that the late Rebbe was Moschiach, and that any prophecies not actually fulfilled by him in his lifetime will be fulfilled in a second coming (some followers say “right idea, wrong guy” to Christians). Of course, they are not officially a separate religion – but not a few Rabbis think that they should be, as they follow someone who, from the strict point of view, is another failed messiah, as he did not fulfill ALL of the prophecies deemed messianic by Judaism. (A note for my Christian readers – these are not necessarily the same prophecies as Christians consider fulfilled or to be fulfilled by Jesus).
To my mind, Chabad escaped being declared a separate religion by the skin of their teeth in the late 20th century. If you were to ask me “Why?”, I might guess that by the time the problem was realised, Chabad actually had too large an influence in Judaism (Christianity might have had were it not for the elimination of most of the Jerusalem Church in 65-70 CE) and also by the fact that there was no-one in Chabad with the interests of Justin Martyr in distancing them from the rest of Judaism.
If nothing else, I think a study of Menachem Schneerson and Chabad casts an interesting light on how Christianity might have developed.