Legal Question in Constitutional Law in Texas

Re: Religion

Private companies may do as they like provided that they don't violate any laws, infringe on anyone's rights or violate their own charters. Christmas parties are seldom a problem.

Your question may arise from concern about the First Amendment's guarantees of religious freedom. Those guarantees are binding on government entities and on public accommodations, but basically not on anyone else. The widely-used description of the rule is, after all, "separation of church and state", not "separation of church and company".

Given our multicultural society, having a "Holiday party" instead of a "Christmas party" seems like the wiser and more sensitive way to proceed. But the law does not require wisdom or sensitivity, and a company can have a Christmas party if it wants.