(Heavily dependent on Brown:)
Here's what Judaism and Christianity have in common:
a. monotheism
b. personhood of God
c. verbal revelation
d. God intervenes in human history
e. the coming judgement
f. ethical rigor
g. moral obligation
Here is where Judaism and Christianity diverge:
Judaism has moral obligation and the 600 odd commandments because God delivered them from captivity
Christianity has moral obligation because of the Resurrection
With Christianity comes quite an assemblage of dogma
The difference between Paganism and Christianity:
Pagan - what is truth? John 18:38
Christianity - I am the . . . truth . . . John 14:6
There might be some Pharisee attitude in this, as well as some of the rest of the Essenes, the Zealots, and the Sadducees. Whether we need an intermediary or can speak directly with God and what the nature of the intermediary (BVM, Christ, local functionary) might be seems to be a moot point among various flavors of monotheists.
Sez you. I think the claim that Jesus was the messiah, and that Christians seek to prove this claim by (mis)using the Hebrew scriptures, prove rather conclusively that it is a material question. If Jesus isn't Jewish, then he sure as heck ain't the messiah. You can kiss the Christian grounding in Jewish scripture and prophecy goodbye.