Insofar as religion in the past was the bedrock of (not only American) society, yes, Thanksgiving can be considered a religious/Christian holiday. But in fact the American Thanksgiving developed essentially as a New World continuation of the old English harvest-home celebration (itself a continuation of pre-Christian pagan traditions), crossed with the British secular tradition of proclaiming thanksgivings to mark important political occasions. The Puritans were dragged into this tradition in the mid-nineteenth century, as part of a general movement that effected a mythologizing of the New England past, in the course of which its specific local traditions and values were transformed into national ones. But the so-called "First Thanksgiving" celebrated by the Pilgrims was a straightforward harvest-home festival (rather ironically, a type of celebration that they in theory abhorred), and definitely not what they understood a Thanksgiving to be (a one-off event marking a miraculous manifestation of God's providence).
Until the mid-nineteenth century there were dozens, perhaps hundreds, of Thanksgivings being celebrated on different dates in different places. The transformation of these many "Thanksgivings" into "Thanksgiving" was largely the work of Sarah Josepha Hale, a bluestocking and editor of the most influential women's periodical at the time. For forty years she wrote and lectured on the need for a national Thanksgiving and badgered every Governor and President without mercy, until finally in 1863 Lincoln succumbed and proclaimed the first national Thanksgiving.
What is interesting is that Hale's aim was both patriotic - this would be a great, distinctive American holiday - and gender-oriented. The only two national holidays at the time were Washington's birthday, which Hale considered an occasion to celebrate the "masculine" sphere of public action, and Independence Day, July 4, which she viewed as commemorating the gender-neutral world of freedoms and rights. Hale wanted to round these off with Thanksgiving, which in her eyes was an occasion to celebrate the private, "feminine" sphere. It is no coincidence, either, that in the years leading up to the Civil War, Hale argued with eloquent zeal for the need to institute a national Thanksgiving, in which the whole American "family", North and South, would participate. In later years, she even spoke of the need to make the holiday universal, with the inclusive warmth of the American Thanksgiving going global. And (aside from that last aim) she was, in the end, successful: to this day, Thanksgiving is the pre-eminent occasion on which all Americans everywhere gather together as families, or families-for-the-day. But religion was not the driving force behind the creation of the American Thanksgiving - these were patriotism and feminism. Thanksgiving, in the broadest sense, has been fueled by ideology.
