I agree with your sentiments about the term "Judeo-Christian". The underlying tenets which qualify are either from the Jewish texts or not. If Christians want to appropriate the Jewish texts then don't try to rope Judaism in as if it condones the new version.
I am looking (maybe wrongly) at how the Jews of the 1st century AD would have viewed John the Baptist & how they view him today if they ever did have an opinion at all, and how christian view him today.
The first thing to point out is this notion of "the baptist." The idea of "baptism" comes from a Jewish idea of ritual immersion. This was done in a particular type of body of water, at very specific times for particular reasons. It didn't require anyone else's intervention - the individual immerses himself. So Jews at the time would not understand someone's interest in (transitively) "baptizing" someone else.
If for instance John was a priest ( and there are some biblical indications that he was)then would mean John was also a messiah from a Jewish stand point?
Christians say a lot about John and it always fascinates me that they say a lot more about John than the bible itself has to say about him.
If John was from the proper family/lineage to be a "priest" then that is what his caste would be. He would not have been anointed, nor COULD he be the messiah in any other sense.
Christians in the beginning of the church were Jewish people. They were not Gentiles. It is understandable why the Christians continued in the Jewish traditions in the first place and why they consider the term Judeo-Christian appropriate. It is not primarily a GENTILE religion. The Christian point of view is that the Christians are the continuation of the OT covenant people. We take the view that the OT Jew and the modern day Jew - and especially since the Temple was destroyed in or around AD 70 are quite distinct from each other.
The Christian position is that Jesus is the Messiah prophesied about in the OT. That this was recognized by some Jews at the time and that other Jews rejected him. When the temple was destroyed - it vindicated the Messiah's prophecy in the Gospels - and as such the Jewish world split into two. Those who were still waiting for the Messiah but without a temple and those who had realized the Messiah - who himself became the living temple. Understandable both sides disagreed with each other's position.
The prophecies relating to Abraham that he would be the father of many nations and that in him all nations of the world would be blessed - indicated that when the Messiah came - the uniqueness of Israel would have fulfilled its purpose - i.e. to reveal the Messiah. Hence the promise was first to the Jew. And why Jews were the first Christians. Yet, it also revealed that the Messiah would break down the walls of ethnicity and extend the promise of God to all nations. Hence Christians, first were Jews and then they extended and ingrafted into the covenant - Gentiles. Gentiles who previously were considered unclean. This was the entire purpose for the dream that Peter had with the sheet of food coming down from heaven.
It is also why there was so many disagreements in the early churches between the proper balance between Jewish law and the grace that came in Christ.
Paul, in his landmark text Romans beautifully explains the differences in the law and grace. Demonstrating that the child of promise ISAAC, was given by faith not by works.
Christians would focus more on the OT by itself that they would on the oral traditions. Interestingly, we would read the oral traditions - and they can give light to many of the scriptures - but unlike the Jewish modern tradition - we do not put the oral traditions on the same level as the Scriptures themselves. And I would think the Jews themselves give lip service to this idea as well. After all, they use the traditions to interpret the scriptures - not the scriptures to interpret the traditions. Still that is a matter for the Jewish religion.
