The movie "Groundhog Day" has pretty much been established as an American Classic. It is perfectly structured, expertly written & directed by one of the nation's funniest guys, starring a man who was at the peak of his comedic and acting career, and clean enough for the whole family. I am not saying everyone should like it. There are many established American Classic movies I don't enjoy at all. I'm just saying that it is no ordinary movie. The use of the holiday of Groundhog Day is mostly incidental to the movie; more of a plot hook than anything, though the theme of rebirth runs through both the day and the movie.
As for religious connections, there is one obvious one. Weatherman Phil at one point decides he must be a God, since he is unable to die. He is confronted with stark reality when he is repeatedly unable to save the life of an old gentleman whose time has come. This revelation is what finally deflates his enormous ego and puts him on a new life path, which eventually leads to his redemption.