Once again. "There were no Jewish-Christians or Christian-Jews." The Jews who followed Jesus were not Christians because Christianity did not exist during Jesus' lifetime. Jesus never even dreamed that Christianity would ever rise. He never saw Paul or a single Christian in his short life. The Jews who followed Jesus were either members of the Sect of the Nazarenes or associated to it as some of the Pharisees. (Acts 15:5-7)
To use a Jew as Jesus was and turn him into a Greek demigod in order to promote a Hellenistic religion, that's an anti-Jewish gospel with the intent on Replacement Theology. Read Mat. 1:18. A demigod was a Greek concept of the son of a god with an earthly woman. In the case of Jesus, God with Mary.
Jesus did speak to Jews all his life but never with a single Christian as they did not exist at his time. Besides, Jesus never spoke to Paul.
It seems that the confusion here is one based on a misunderstanding of a term. We both agree that Christianity didn't exist during the lifetime of Jesus. Christianity is something that evolved later on. We don't disagree there.
The term Christian arose in Antioch, at some point before the book of Acts was written. It literally meant Christ follower. A follower of Christ, or a follower of Jesus. When I use the term Jewish-Christian, which is an accepted term in the scholarship, I'm referring to Jews who followed the message of Jesus. Jews who saw Jesus as the Messiah.
Throughout history, different groups of Jews have acknowledged various messiahs. Jesus just happened to be one of them. Generally, when the so-called messiah dies, people realize that that wasn't the messiah, they were wrong, and the movement dies out. For whatever reason, that didn't happen when Jesus died. Some of those who saw him as the messiah continued to do so after his death, and continued to follow his teachings. They were Jews who followed Jesus as the Messiah, as Christ.
The first followers of Jesus were labeled Christians, probably by Roman authorities, in order to differentiate them from other groups of Jews. In essence, Christianity just became another sect within Judaism. It was just a sect that saw Jesus as the Messiah, which fit within Judaism at that time.
It wasn't until after the Jewish revolt, and the destruction of the Temple, that a split really happened. On one side, there was the Pharisees, who became Rabbinical Judaism. On the other side, there were the Jews who saw Jesus as the messiah. Eventually, the movement itself became more Gentiles than Jews. However, we do have evidence that until at least the fourth century, there were groups of Jews, what are referred to as Jewish-Christians, who continued to see Jesus as the Messiah.
So yes, there were Jewish-Christians, as in Jews who considered Jesus to be the Messiah.
You keep speaking of the sect of the Nazarenes; however, what you fail to mention is that Acts tells us that Paul was the leader of that sect. In fact, that is basically the only thing we are told about the Nazarenes. Why don't you address that? Because as it stands, everything else you say about the Nazarenes is simply made up, or unfounded. Acts only mentions the term Nazarenes once, and in doing so, says that Paul was a leader of that sect.
As for the talk about Jesus being a demigod, not according to Christian teaching. First, Paul never states that Jesus was born of a virgin and of G-d. So he wasn't spreading that message.
In Christian thought, Jesus was considered G-d. So not a demigod.
With Matthew, and Luke for that matter, the stories weren't meant to be taken literally. That's why everything in the birth narratives never are mentioned elsewhere. They seem to exist in bubbles. Looking at ancient traditions, including Hebrew tradition, birth narratives were generally crafted after the person became important, as the idea was that if one was important as an adult, their birth would have also been of importance. Because of that, births were wrapped in mythology that more contained theology than what was meant to be taken as fact.
We can look at the birth narrative in Matthew, and see that it largely resembles the birth of Moses. Why? Because the author of Matthew was arguing that Jesus was the new Moses. But seeing Jesus as more important, his birth had to be more spectacular. Thus, a virgin birth was created. It wasn't meant to be taken literally though, and by far, it wouldn't be until much later that Jesus was thought to be the literal son of G-d.
Context is everything here.