Here's a few days worth of movies that were playing on or around Thanksgiving over the years. Unlike at Christmastime, these are mostly not films with holiday themes, but they are often family movies or films getting an early shot at holiday traffic.
Opening in time for Thanksgiving viewing in New York in 1933 was Design for Living, a witty and sophisticated romp based on a play by Noel Coward. He complained that the screenplay was a complete rewrite of his story of an attempt at a long-term threesome, but it still has its moments. It was playing at the Criterion, and coincidentally, the movie was released on DVD as part of the Criterion Collection.
For less high-class comedy, you could see Duck Soup, the Marx Brothers classic, over Thanksgiving. The top ad is from New York, the bottom from Atlanta the week after Thanksgiving. At the time, the movie was not a box office hit like their earlier ones were, but it is now considered their funniest. I like Animal Crackers more, but this one will do.
A Busby Berkeley musical spectacle, Footlight Parade, also opened in Manhattan for Thanksgiving, complete with live vaudeville acts, though I suspect none of the live performers could outdo the production numbers that Berkeley put on the screen.
Finally, the legendary Mae West, in one of her last hit movies before the Production Code came into effect next year and tamed her ribaldry.