Ehh seem would cause waining in crusading support and the fantical catholtic lords in the holy lands would not be up for it esspically with an increasing catholtic presence
A different Rite is not a different Church. A Liturgical Rite is, well, its a bunch of stuff: but it's basically the form of Mass which develops as well as other aspects to how the Church interacts with the life of its members.
For instance, the OTL Byzantine Rite Catholics are in full communion with the Catholic Church. However their masses are done largely following the Greek Orthodox liturgy, priests (but not bishops) are allowed to marry, etc. In OTL, the Catholic Church has always contained a number of different Rites - though the Roman Rote became the dominant one during the Middle Ages, it was never the only one.
When I'm saying the development of a Jerusalem Rite, this is what I'm talking about. They are going to be at a crossroads with many other Christian communities around, some stronger, some weaker, and it's only natural that this would lead to some evolution in the local Catholic Church that would, at some point, be eventually codified.
It would actually be less likely that there would be no influence from other communities, evolution, or local developments than it would for this to happen, in my opinion.
And, as to absorbing other Christian communities - the name Catholic says it is: it seems itself as the One Church. It won't budge on theological matters, but as to the form of Mass and other things which doesn't deviate or undermine foundational doctrine? Historically, those are areas where the Church is capable of some compromise if it brings a group into communion with Rome (So, as an example: Rome would never compromise on an issue as important as the nature of the Trinity - that's a foundational doctrine. But they have shown themselves, even up to the modern day, to enter into communion with a Church which says its liturgy in, say, Aramiac and allows for married priests.=