This statement is not correct. Reb Moshe has repeatedly stated that
Thanksgiving is in fact not a religious holiday. The position of Reb Moshe
is presented in the Igros Moshe Y.D. IV #12 and Orech Chaim V #20.6 and
Y.D. IV #11.4 as well as Even HaEzer II #13.
He writes in Orech Chaim V #20.6 (the new volume). "In regards to
Thanksgiving, I have already written Even HaEzer II #13 that according to
the straight law there is no basis to prohibit a celebration of any event
on this day, e.g., Bar Mitzva or wedding - but a Baal Nefesh should be
machmir (more strict). But to make a celebration and meal in honor of
Thanksgiving this should definitely be prohibited. Not because there is a
concern that it will appear as celebrating a religious holiday - because
this is not a holiday established by a religious group for religious
reasons..."
Daniel Eidensohn