Brunaburh
Gone Fishin'
Yet, by the Ottoman period, Jews had already become a large percentage in the cities of Tiberius, Jerusalem, etc... Judaiism was by 1526 the largest single group in Jerusalem followed then by Christians and then by Muslim of the Sunni variety. If the Jews already seemingly where the majority of some of the city populations, then it is not inconceivable for them to also be of a high percentage. Especially considering that Palestine has the smallest population of any of these areas, most of which under Arab rule is just Bedouin and walked forts.
For the city of Jerusalem, yes it is plausible that a third were Jewish at some point in the early 13th century. I doubt it though, given the fact the Jewish population was murdered en masse in 1099, and I don't think the KOJ was the friendliest place to Jews. Do you know anything about the Jewish population of Jerusalem at the time it fell to Saladin? I suspect it would require a very quick repopulation to get 33% by the early 13th.
Under Ottoman rule it is of course unsurprising that there were moments where Jews were a plurality though they frequently converted to Islam, there are a lot of Palestinian Arab families of Jewish origin.