We are not Christians, and we aren't particularly enamored of the capitalist version of the festival that has taken over either.
Why should we allow our kids to be sucked into the hype, and have their expectations influenced by multi million pound advertising campaigns when we can choose for ourselves when to have a big dinner and give/receive gifts?
We played with replacing the gift giving part with a Samhain festivity, but have now instituted a Presents Day, in the new year. We have a family gathering, big dinner, and exchange of presents. This also allows us to take advantage of the lower prices (Post Xmas) at this time of year.
No pseudo religious symbology, no purchase hype, but we keep the good parts: presents, get together, dine big.