minyan gal, the founders of this country were proud Christians, and since their concept of “God” is the trinity while yours, lihavdil, is not, what they did at that first Thanksgiving is certainly NOT what we do every Friday night and Yom Tov.
On another note, we thank Hashem at daily tefillos and other occasions, not the once a year we get around to it, so it is at least inappropriate for that reason. (Similarly, Mother’s Day and Father’s Day are also not up to par.)
July 4th, on the other hand, is completely secular and national so Christianity has nothing to do with it, presumably. Having said that, that doesn’t mean it’s therefore a mitzva to celebrate it, but simply celebrating/BBQing in a dignified manner, preferably as a seudas mitzvah, would seem to be appropriate Hakaras HaTov to this Medina Shel Chessed. Ask your LOR, of course.