IDEAS & practices of the Jesus movement of the first century and the beginning of the second century ~ & even later ~ can be safely under-stood as part of the ideas & practices that we understand to be the Judaism of this period.
The ideas of Trinity & incarnation, or certainly the germs of those ideas, we're already present among Jewish believers well before Jesus came on the scene to incarnate in himself, as it were, those theological notions & take up his messianic calling.
However, the Jewish background of the ideas of the Jesus movement is only one piece of the new picture we're sketching here. Much of the most compelling evidence for the Jewishness of the early Jesus communities comes from the Gospels themselves. The Gospels, of course, are almost always understood as the marker of a very great break from Judaism. Over and over, we find within interpretations of them (whether pious or scholarly) statements of what a radical break is constituted by Jesus' teaching with respect to the "Judaism" of his day.
The notions of Judaism as legalistic & rule-bound, as a grim realm of religious anxiety versus Jesus' completely new teaching of love & faith, die very hard. Even among those who recognize that Jesus himself may very well have been a pious Jew ~ a special teacher, to be sure, but not one instituting a consequential break with Judaism ~ the Gospels, & especially Mark, are taken as the sign of the rupture of Christianity, of its near-total overturn, of the forms of traditional piety.
One of the most radical of these displacements is, according to nearly all views, the total rejection by Mark's Jesus of Jewish dietary practices, the kosher rules? Counter to most views of the matter, according to the Gospel of Mark, Jesus kept kosher, which is to say that he saw him-self not as abrogating the Torah but as defending it.
There was controversy with some other Jewish leaders as to how best to observe the Law, but none, we will argue, about WHETHER to observe it. According to Mark (& Matai even more so), far from abandoning the laws & prac-tides of the Torah, Yeshu was a staunch defender of the Torah against what he perceived to be threats to it from the Pharisees!