May I ask you something?
I was brought up in the Christian faith so I have a loose understanding of their old testament.
Are Muslims the descendants of Abraham?
many of the arabs are the literal descendents of Abraham, from his first born son ishmael (peace be upon them both), the prophet muhammad (pbuh) being the most famous such decendent.
but all muslims are following the same message of abraham, to preach the message of monotheism, indeed we claim every prophet of God is muslim, they are all following the islam of their day.
Ibrahim was not a Jew nor a Christian but he was (an) upright (man), a Muslim, and he was not one of the polytheists.
Quran 3:67
a Muslim is a person submitting to God, coming from the route word in arabic meaning to submit, so islam is the way of submission to God and a muslim is a person who submits.