... obscure links to other religions and traditions...
Judaism in Jesus' time was not monolithic. The Gospels mention several factions. It is hardly an "obscure link" between early Christianity and Judaism. And if you read later theologians, the influence of Greek philosophy is also hardly obscure.
Regardless of my position on Christology, these links are just plain obvious.
And the do not detract from Jesus' teachings either. He put them forth in Jewish terms, later Generations used Greek philosophy, scienctific terms, even computer science is nowadays a source of words for the expression of religious/spiritual ideas and sentiments.
Nothing wrong with any of that, to me.