Jewish thinker – B”H that the Goyishe velt finds a day to say grace once a year (though to be fair, religious non-Jew often DO say grace at their meals). If turkey was abundant in the New World, and it was, it makes sense that it was eaten, and the fact that it is a large bird, made it economical for the Pilgrims to feed a large family with one turkey. That’s probably why it was so popular.
On Thanksgiving, we do not see and religious symbols in the media, in the decorations, etc. The Pilgrims came here searching for freedom from religious persecution (sound familiar?), and as Jews we can and should identify with that. We came to the US for similar reasons after WWII. So we are very much a nation of pilgrims, too.