Is there any issue with Jews wishing each other "Happy Thanksgiving" or "Happy Turkey Day"?
This sums it up nicely:
To most American Jews, even most Orthodox Jews, there is no question about the appropriateness of celebrating to Thanksgiving; to them, it is a secular holiday that represents values important in Judaism and in American culture. To many traditionalist Jews, however, commemorating any non-Jewish holiday raises questions about biblical and rabbinic law forbidding Jews to imitate non-Jewish customs and traditions.
Chabad do consider Gd to be part of Thanksgiving (Gd being who we're giving thanks to.) So in that way it's not completely secular. None the less, it is not proscribed as part of any group's religion and not given religious symbolic meaning.
The Chabad then point to a similar concept of thanksgiving in Judaism called bikkurim, that adds to it a act to reinforce the appreciation: