Christians and Muslims come from many ethnic and racial backgrounds. The only person they are all descended from is Adam.
At some point in history, the idea became popular that Arabs are descendants of Ishmael, and Jews are descendants of Isaac. Obviously not all Arabs are really descendants of Ishmael and it seems questionable for all Jews too, so it shouldn't be interpreted as a literal fact. Anyway, most Muslims are not Arabs so this does not factor into questions of descent.
There are texts identifying the Prophet Muhammad as a descendant of Ishmael so this may be another way of associating Islam with Ishmael. Also Muslims tend to say that Ishmael was the son of Abraham whom God asked him to sacrifice (I sense another complicated question coming...) whereas Christians and Jews say it was Isaac. So, again, one can say there is a sort of figurative association or inclination towards each.
Of course, both Isaac and Ishmael are respected in the Islamic tradition and in the Qur'an.