There is no law that I am aware of that tells a Home Owners’ Association what type of party it must hold during December holidays.  An HOA acts through its board of directors and its members and can hold whatever type of party it wishes — or no party at all. 

Since an HOA governs a social association and not a religious association, I tend to favor a more inclusive approach recognizing the different traditions and beliefs of as many members as possible, including the growing number of Americans who express no religious preference at all.  If you can’t convince the board to broaden the party voluntarily, the decision is ultimately made by directors who are elected by the members.  If enough members don’t like having a party relating only to Christmas, they can try to elect new directors who will take a broader view, or perhaps prohibit expenditures for a “Christmas party” in the Association’s budget if they get to vote on the budget.  In the meantime, they can simply stay home if they don’t wish to participate.  I think it is a shame, however, when an event intended to celebrate a festive season ends up dividing the members instead of uniting them.