I can understand the appeal of a messiah in 1600s Eastern Europe. I can understand that we want a messiah and we're willing to accept one, whether it be Bar Kochva or Shabbtai Tsvi.
But on what sources could people possibly have held that Shabbtai Tsvi was the messiah:
- after he broke most of halakha?
- even after he converted to Islam?
- even after he died?