The censuses were always flip-flopping back and forth, until the 1880s. You cherry picked one nice one, but I could check pick over half a dozen censuses that show Jewish majority during the 19th century - no less than the amount of censuses that promote the other competing narrative. And all the later censuses, after 1880, show Jewish majority. That was over three decades before the fall of the Ottoman empire.

  Source for census data:
  https://en.m.wikipedia.org/wiki/Demographic_history_of_Jerusalem