Yeah, I personally would like to emphasize the celebratory tradition over the mythological tradition. But that's probably why this is all best left to the individual. When I think of Christmas, I think of hearth, home, tearing open presents as a kid, etc. Now it's a time to watch football and drink a lot of wine and see people I don't routinely see. So if it has mythological importance to you, fine, but it does not to me. I think secularists would probably just like for that to be respected.
Christmas songs are not religious?
Santa Baby, Jingle Bell Rock, Winter Wonderland, Frosty the Snowman, Up on the Rooftop, et. al. hundreds and hundreds routinely played on the radio right now are not, no.