Yes, and there was a lot of mixing and slow but gradual conversion to the dominant socio-cultural muslim group that happened over more than a millenium. After the muslim conquest of Levant in about 630 AD, caliph Umar ibn al-Khattab lifted the Christian ban on Jews entering Jerusalem some time later during his reign. We do not have data on how many jews decided to return there, rather than keep living in civilizational centres across the region and in Europe.

What we do know is that the jewish population of Palestine at the time that the British government initiated the process of handing over Palestine to jews in return for Lord Rothschild's money that they needed to keep fighting WW1 [2], was only about 7%. Subsequent immigration of mostly European jews into Palestine, resulted in about 30% jewish population by the time Western powers decided to declare an independent Jewish-dominated state of Israel on top of Palestine in 1947.

> Both have a right to exist and the capacity to live peacefully together

Brutal occupation has no right to exist. The supremacist state has to go. Apartheid South Africa had to go, and now South Africa is a better country. Nazi Germany had to go, and now Germany is a better country. Imperial colonial Japan had to go, and now both itself and its former colonized territories are better countries. Supremacist ethno-nationalist Israel that occupies natives of the land it was established upon with despicable brutality has to go. In the resulting state that comes after it, yes, people of any religion and ethnicity need to be able to live together in peace. After reparations have been made, the right of return has been honored, most of the stolen land has been given back, and apartheid has been dismantled.

[1] https://en.wikipedia.org/wiki/Umar

[2] https://en.wikipedia.org/wiki/Balfour_Declaration