Many such communities existed into the 20th century, but they overwhelmingly emigrated to Israel amidst mounting persecution and violence following the war of 1948, and in a second smaller wave following the Six day war.

This varies on a country by country basis, only about one third of Iran's Jewish community left after Israel declared statehood, with a much larger exodus after the revolution in 1979 to both Israel and the US.

Most estimates count 800,000-850,000 refugees/emigrants to Israel from Arab countries between 1948-1980. The degree to which they fled or willingly emigrated is complicated and contested, and also varies between countries and communities. But the violence and persecution were widespread, and in many cases had been increasing for decades.

This excellent answer by /u/ghostofherzl discusses this process in depth.

Your statement that "Muslim ruled kingdoms on average were more tolerant" is true to a large extent right up to the 20th century. But Jewish communities in the Muslim world also faced discrimination and violence, which became quite severe in the early 20th century, even prior to Israeli statehood.

These dynamics are discussed in another excellent response by the same author here and added to with a response here.