What movement arose to challenge the elitist practices of the Catholic Church?

The answer to the question above is the Protestant Reformation.

Protestant Reformation, also known as Reformation, was started by Martin Luther in 16th century when he posted the Ninety-five Theses in 1517. John Calvin, Huldrych Zwingli, and other Protestant Reformers continued what Martin Luther started until the Reformation lasted in 1648 during the Thirty Years' War.