Well, I come from a deeply religious pagan background in the old-fashioned sense (Hindu 'unbeliever') and then turned atheist, but I also have a neo-pagan (not quite Neo Pagan) seasons-celebrating streak. And I grew up celebrating Xmas --- the trees and Santas and plumcakes aspect of it more than the presents, which were non-existent or token --- at school (Methodist Church) and at home (Anglophile colonial hangover?). It's sort of 'traditional' for me.
So I obviously don't celebrate Christmas in any religious sense, but you might say I celebrate the solstice/mid-winter itself as Yule. Most years I do make a point to bake and feed a 'Christmas' cake (not this time); even if I don't have a tree, I do put up lights and hang up ornaments. Again, it's the seasonal aspects of the celebration I hang on to. A few years, we've had parties with friends that involved gift giving. Mostly, however, not.
Lots of wintry 'special foods' get cooked and bought though, right through the Advent season and up to Orthodox Christmas --- this is the norm in my hometown, where there are substantial Christian (both Eastern/Orthodox churches like the Armenian as well as Catholic and Protestant) and Jewish communities.
In a way, at a personal level, it is not very different from ways in which I mark the vernacular harvest celebrations or the first day of spring or the time around Halloween/Diwali/Autumn Moon when many cultures seem to honour their ancestors who've passed on. There are special foods, little rituals of acknowledgement and thanksgiving and remembrance for all of these, which I see as cultural, possibly a little spiritual and not at all religious.
it's just that at this time of year, my 'celebration' is more visible and emphatic because people around me can and do join in, and they notice my activities almost because they're expecting this sort of activity around them. Which makes it more... festive?