Glomung

"Judaism and Christianity come from the same book (TORAH-BIBLE),
yet the beliefs are 180 degrees apart from one another. "

Not really true.
Most Christian practice is based on the New Testament. We
are freed from the Old Covenant and live in the New Covenant.

"How did Christianity grow so estranged from Judaism when
the Messiah was a Jewish Rabbi, the Gospel was to go out
to the "Jews first", and not to the Gentiles (MAT 10:5-7)."

He was not "a Jewish Rabbi" he is "God in the flesh". He went first
to the Jews because God the Father had a covenant with them. It was
only after refusal on the part of the Jewish leadership that the door
was opened to the gentiles.

"How did the biblically ordained festivals like Yom Kippur,
Sabbath and Passover get replaced by unbiblical festivals like
Christmas, Easter and Sunrise Service which are all rooted in
Pagan tradition and history?"

Christmas was originally set at that time to compete with pagan festivals,
a way to keep the followers out of trouble. Later it became mixed with
traditions from various countries and now commercialized to the point that
it's hard to recognize. Easter was the "best guess" as to the date.
There is nothing pagan about sunrise services. It's just starting the day
with God.

"What is the biblical reason Judaism discounts the authenticity of Jesus?"

The Jews have always looked for a Messiah that would conquer all non-Jews and make them (the Jews) the rulers of the physical world. Since Jesus did not destroy their enemies, but instead said to "love your adversary" the Jews would have none of it. Jesus did not fulfill their notion of what the Messiah would be, so thay have refused him to this day.

My 2 cents, Glomung