And this is present even in Trinitarian beliefs. God the Father is the very same as God the Son (who is God the Father manifest in the flesh here on Earth,) who is the very same as God the Spirit (who is the breath of life and divine essence of god within all living things.)
It's also been addressed that Christianity quite selectively "accepts" Jewish theology. More often than not it changes and "updates" the theology, just as Islam did with both before it. They are all three Abrahamic in that they worship Yahweh, the god of Abraham.
An issue which is non-existent. If Islam's concepts regarding Yahweh are the exact same, then Christianity accepts and/rejects them on the very same level. Even by claiming and believing that Jesus is the Messiah, the son of Yahweh, Christianity diverges from Jewish theology significantly. Their portrayal of Satan as some villainous, evil spirit (of which Islam does too,) also separates from the Jewish theology regarding Satan.
So your issue seems very fuzzy. It's not like Christians are playing favorites with who they take cues from (which is where the chronology comes in; why would Christianity take inspiration from a later religion?), and they've changed quite a bit of Jewish theology to where it can't really be said that they're accepting it. Neither are Christians rejecting Islamic theology concerning the nature of Yahweh; the prophethood of Mohammed isn't a theological issue per se. This just seems to be yet another "those poor misunderstood and theologically bullied Muslims" thread.