However, birth rates are more correlated to wealth, not to religion. Poorer people have more kids than wealthier people. Palestine is much poorer than Israel, partly because of the constant war and unrest there, as well as the lack of a strong state apparatus. This means nobody wants to invest money to start businesses and create good jobs Meanwhile, Israeli companies and people exploit this by hiring Palestinian workers at very low wages.
Palestine is also beholden to the monetary policy of Israel as they are forbidden by treaty from establishing a national currency. Thus, the currency of Palestine is largely the Israeli new shekel.
Once there is peace, there can be work to fix these problems and increase the living standards of Palestinians. Once that happens, history tells us that their birth rate will naturally decline.
You’re probably right. At the same time, stability and the right environment for business can do wonders for a country’s economy. Just compare the dirt-poor China that Deng Xiaoping opened to global investment and the now-dominant regional superpower of today.