Unlike Christianity, there was no "bible" from which Abraham got his theology. There was no acceptance of Jesus as Messiah. There was no Messianic resurrection account in Abraham's belief system. There was no salvation by grace through faith as he sought salvation through works. There was no belief in a trinitarian concept of deity. Christians view their lineage through Abraham through faith alone yet he saw lineage as biological.
Abrahamic faith was so obscure that to this day, the top three major religions claim Abraham as founder. So if Abraham can be considered Muslim AND Jew, he couldn't have been Christian enough.