The Venerable Bede, in his Ecclesiastical History of the English People , tells the story of King Edwin, who had embraced Christianity primarily because he thought he would become a great and powerful king as a result. And Bede says, in fact, he did. But he also noted that Edwin was, and always had been, a thoughtful man who would sit by himself hour after hour pondering the deep mysteries of life. Later on, after Edwin had become king and was growing in power, he ran into a missionary who was this same mysterious stranger whom he'd had seen in his vision years earlier. There was in Edwin a desire for salvation, and he felt that beyond the wealth and power Christianity gave him, it also helped him settle this issue in his own heart and mind.
Today using force to convert is unthinkable.
That being said, my hunch is that it's largely due to the rise of Protestant evangelical movements, especially the Great Awakening. Here we see a new stress placed upon the individual soul and upon religious experience. Conversion becomes a voluntary, individual turning to God. Once you have that understanding, the idea of forcing someone to convert becomes absurd. Jesus, the foundation stave.