The origin and text of the (not legally binding) proclamation each year clearly suggest a religious order. The question needs to be asked that if goyim hold a yuntuf in order to (and to give thanks to) the Ribbono Shel Olam (and make a point of not mentioning any false gods, but clearly giving thanks to Ha-Shem) if the prohibition of avodah zarah applied.
If at some point the Americans elect an openly atheist President, who says the holiday is to celebrate prosperity by shopping, with no reference thanking anyone other than themselves, it would clearly no longer be Avodah Zarah. So perhaps by 2021 if the Democrat’s Blue Wave turns American into a socialist paradise, we won’t have a shailoh.