1. One side would argue that it is similar to the “King’s birthday”, for which frum Jews in the past did join in the celebration (especially if we liked the king in question). What make’s Thanksgiving different is the President’s tradition of declaring that it is a quasi-religious holiday .
2. The origins going back to colonial times were that days of Thanksgiving were religious holidays, though never tied to a specific religion or denomination (always careful to avoid anything to insult any specific religious group, while probably insulting atheists though that isn’t an issue for us). If one holds that when Christians talk about the “creator” references in Breishis they are talking about Ha-Shem rather than a pagan diety, that eliminates some of the objections. One should ask if a frum political leader could call for a day of Thanksgiving for some national deliverance and ask Christians and Muslim (but not atheists) to join us. It should be noted that the connection to Plymouth in the 17th century in declaring a day of Thanksgiving is ahistorical. (at most a precedent, but more of a gimmick).
3, Unlike some non-Jewish holidays (particularly the one based on the Roman Saturnalia, which includes the pagan custom of having a tree in one’s house), eating a turkey or playing flag football do not seem to have religious meaning. Honoring the the 17th century colonists in Plymouth (who were quite anti-Semitic) seems problematic (though accusing them of genocide is a stretch since most of the locals were killed be infectious diseases that neither side understood how they spread). There is prohibition of imitating goyim