One idea: Celebrate it on December 23. If they want to bash the holiday and those who celebrate it as "pagan", let's go all out and use the original Pagan date and do it then. Exchange the gifts on December 23, and have all the festivities then. Then, when December 25 comes, they can go to all boasting sessions and tell the hounders that they are not celebrating Christmas. All, technically without lying because they are celebrating Yule, not Christmas.
In this situation, everyone except joke-hova wins. The congregation gets the "no Christmas", the children get their presents (2 days earlier than everyone else, to boot), and the proper Yule date is observed. And, while they are at it, they can move the other holidays to their proper places and celebrate those as the Pagan religions once did. Easter can be moved to the Vernal Equinox--Astaroth's Day. Lammas Day can be celebrated in much the same way Kwanzaa is today--the first of August. (It is the day of the harvest.) About the only holiday that this will not work well with is Halloween, because that is relatively unchanged and the date is still October 31.