Rabbi Moshe Feinstein in Igros Moshe Even Ha'Ezer 2 #13 says (my translation):
One should not plan a simcha on a non-Jewish religious holiday. If it was planned specifically for that day because it is their holiday, then by letter of the law it is assur. If it happened to come out then, it should still be assur due to maaris ayin.
A seudas Mitzvah like a bris or pidyon haben one could make even on their holiday, because we should not make assur a seuda that is incumbent upon us due to maaris ayin. Whereas a Bar Mitzvah should be pushed off for another day, and a wedding too should be planned originally for another day.
New years and Thanksgiving is not assur by letter of the law but a baal nefesh should be stringent.
My question is what about a Chanukah party on Christmas. The poskim all say a chunakah party is not a seudas mitzvah, but at the same time perhaps perhaps the day forces our hand, like a bris or pidyon haben. Of course it is not exactly the same, there you have one day here eight, but those eight days are not completely up in the air to choose like a bar mitzvah or wedding.
(E.C. Also, are there any more modern responsa dealing with this mar'is ayin? I don't really understand how this maaris ayin works.)