Why do many Jews adopt the Muslim narrative that they are the children of Ishmael with an unbroken lineage from Abraham?

I always find it strange that many Jews/Rabbis accept the narrative that Islam and Arabs are the children of Ishmael EDIT and have an unbroken tradition from Abraham. The other common narrative is that Mohammed just read/understood the Torah, and applied the narrative of the children of Ishmael to convince his Arabs brethren that they are important and are part of a long long history as a way to legitimize himself and his ideas. There is nothing inherently wrong with this (The Torah has many places for the world’s nations to build connections to), but from what I know, the consensus is that there was no tradition from Ishmael to Mohammed, and that he made much of it up based on what he saw around him and read.

What do you on r/Judaism thing? Do you accept that Arabs are the children of Ishmael with an unbroken tradition from Abraham?