The nice thing about mythology is that there is never a hard, firm, this is correct version of a story. There were no literalists in Ancient Greek paganism. Euripides told Jason's story different than Apollonius of Rhodes. Aphrodite is born from the severed genitals of Ouranos in some stories, is a daughter of Zeus in others. And so on. There's common cores to these myths (e.g. Aphrodite is always the goddess of sensual/sexual love), but the details can vary incredibly.
And the Christmas Story nices fits. The two Biblical versions have key differences but a common core. And people mash them up in various ways so we got both Shepherds and Wise Men even though the Biblical accounts don't really fit together that neatly.
But the core myth, about a baby being born to bring Hope and Love to the world? Priceless. One of the few things from Christianity that I carry with me. I just don't believe the details of whether Mary was really a virgin or how many Wise Men there were matter that much or was the stable a building or a cave really matter that much at this point in time. It's the story and how we bring it into our lives.