This is a tricky subject on ask historians because the answers touch on more recent politics and because the reasoning behind a choice of phrase often leaves no direct records.
So text searches indicate the phrase becomes seems to appear after 1950 and become more common after 1954.
The starting point here is why a phrase was adopted that links 2 groups of religions rather than one that encompasses all 3 groups of Abrahamic religions, given that all 3 share a holy book, a definition of god and a holy city.
The phrase was very uncommon until after the Second World War. Until then Conservative politicians both in Europe and the US had tended to be anti Semitic to some degree and using aterm that referred positively to Jews would be unusual. Jews were often regarded as being linked to Bolshevism and communism.
After the Second World War there was a completely changed geopolitical climate. As the US and the USSR competed for hegemony the emergence of Israel which became aligned to the US became an important cause. Israel was surrounded by Arab Islamic countries that became aligned with the USSR, partly because of the US alignment with Israel. So Jews were now seen as bulwark against communism and so to be supported.
Developing a term that reinforced identification with Israel and othered Arab states was very useful, particularly when that phrase emphasised an apparent continuity of cultures.