If life were only so simple.
The people who accepted that Jesus (Yeshua) was indeed the promised Messiah - people such as Peter, Paul, Matthew and John - were Jews.
It is always so simple to lump people into pigeon-holes, making a homogenous pie when there are many many separate parts. Take the modern concept of "Christians". This term encompasses the broadest range of ideas and ideals. This was also true of Israelites in the times of the NT Scriptures that they wrote. While many were expecting a warrior-king who would destroy their enemies, others were expecting a human/divine being. There were many at the time claiming to be the promised Messiah, and the question that people asked was: "Is this One the Promised Messiah?" Some Israelites did, and through the perspective of subsequent history, notably the prism of the third century, we view some Israelites as "Jews" and some Israelites as "Christians".
Those Israelites who did accept that the anticipated Messiah (Mesach/Christ) would be a divine/human based their beliefs on the imagery of Daniel 7.
The following is written by a Jewish scholar.
Doug
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Being religiously Jewish then was a much more complicated affair than it is even now. There were no Rabbis yet, and even the priests in Jerusalem and around the countryside were divided among themselves. Not only that, but there were many Jews both in Palestine and outside of it, in places such as Alexandria in Egypt, who had very different ideas about what being a good, devout Jew meant. Some believed that in order to be a kosher Jew you had to believe in a single divine figure and any other belief was simply idol worship. Others believed that God had a divine deputy or emissary or even son, exalted above all the angels, who functioned as an intermediary between God and the world in creation, revelation, and redemption. Many Jews believed that redemption was going to be effected by a human being, an actual hidden scion of the house of David—an Anastasia—who at a certain point would take up the scepter and the sword, defeat Israel's enemies, and return her to her former glory. Others believed that the redemption was going to be effected by that same second divine figure mentioned above and not a human being at all. And still others believed that these two were one and the same, that the Messiah of David would be the divine Redeemer. As I said, a complicated affair. …
Christ too—the divine Messiah—is a Jew. Christology, or the early ideas about Christ, is also a Jewish discourse and not—until much later—an anti-Jewish discourse at all. Many Israelites at the time of Jesus were expecting a Messiah who would be divine and come to earth in the form of a human. Thus the basic underlying thoughts from which both the Trinity and the incarnation grew are there in the very world into which Jesus was born and in which he was first written about in the Gospels of Mark and John. ...
Almost everyone recognizes that the historical Jesus was a Jew who followed ancient Jewish ways. There is also growing recognition that the Gospels themselves and even the letters of Paul are part and parcel of the religion of the People of Israel in the first century A.D. What is less recognized is to what extent the ideas surrounding what we call Christology, the story of Jesus as the divinehuman Messiah, were also part (if not parcel) of Jewish diversity at this time.
The Gospels themselves, when read in the context of other Jewish texts of their times, reveal this very complex diversity and attachment to other variants of "Judaism" at the time. There are traits that bind the Gospel of Matthew to one strain of first-century "Judaism" while other traits bind the Gospel of John to other strains. The same goes for Mark, and even for Luke, which is generally considered the "least Jewish" of the Gospels. (“The Jewish Gospels: The Story of the Jewish Christ”, by Daniel Boyarin, pages 5-6, 22)
