I've had an ambivalent relationship with Christianity all my life. These days, I think it's a lovely idea which has been perverted to cause much anguish and hurt over the centuries. And the same can be said about most religions, frankly. With the possible exception of Buddhism.
That said, I have a great relationship with Christmas music, having loved & collected it all my life. I have no trouble singing "Christ the Saviour is born..." while not being sure that is actually what took place. The music, along with the ideas it represents, are wonderful.
I've praised these women for years, and I'm not going to stop now. The Roches, 3 sisters with serious vocal skills, did a Christmas album in 1990 that I still love, "We Three Kings". Comprising both traditional songs as well as a few lovely originals, it combines the best of the Christmas spirit with their populist folky vocal stylings. While not classically trained, the sisters represent to me the way singing must have been during the middle ages & the Renaissance, technically skillful yet not overly mannered.
Here they are live, singing a medley of several of their versions of traditional Christmas carold:
And if you have any doubts about their vocal skills, listen to them rock Handel's "Hallelujah Chorus" live in '82:
Point is, you don't have to believe the mythology to love the music and the spirit of Christmas.