Trinitarian vs unitarian is a theological difference that requires different definitions and identities of god even if they both use the monotheist label. These are not compatible differences, you would have to believe contradictory beliefs to say one god identity exists and represents both trinitarian and unitarian theologies and is the same god. Just because they share the same name doesn't mean they share the same properties.

The Christian bible disagrees with the Jewish bible unless you apply the Christian apologetic hermeneutics of someone who believes the Christian bible. Instead of saying they're replacing theology they're going to fulfill and expand and enhance, theology+. The anonymously written Christian gospels say Jesus is the messiah but the Jewish bible messianic prophecies say the messiah would be a king who rules on the throne of David that Jesus never did. The Christian bible gospels misquote from the Jewish bible that were not prophecies (born of a virgin vs young girl already pregnant, quoting Zekariah as Jeremiah, etc) because the gospel writers were using a Greek translated version instead of books originally written in Hebrew. It says you don't need to follow the old law and prophets and sacrifices anymore when the Jewish bible says they need to be followed forever. Hell being eternal torture is a clear break from the legacy Jewish dogma.

I'm not educated on the Quran but I'm pretty sure neither Jews nor Christians believe the same theology at Muslims which are derived from their god beliefs, otherwise they would have included the Quran in their bibles too or have books in their dogma about the laws and teachings of Muhammad as a messiah. They can't change the established dogma so they spin up a new religion to change the theology.