I don't think the Parsis were/are seen as a separate group by the Zanzibaris. They were considered a subset of the Indian community (or Gujarati) settled in East Africa. When the revolution took place, hoards of South Asians and Arabs fled the country as they were targeted by rioting mobs. I believe most fled to the United Kingdom, North America, and some even repatriated back to India. Not sure about Parsis in modern day Tanzania, but other South Asian groups seem to be doing well, some of them even occupy top government posts.
Here's a blog I found on Tanzania's Parsi heritage.