I'm not sure I completely understand Dr. Mohler's concern with "determinism," unless it is with the idea that mere genetics, environment, biology or psychology determine our "moral responsibility." This kind of material determinism is typical of "science" today.
But Dr. Mohler, in a sense, affirms a determinism much more potent and controlling as any envisioned by a secular scientist. This "spiritual determinism" is also known as "double predestination," or the belief that GOD "determines" all things, including man's "moral responsibility." Mohler and other adherents to this "spiritual determinism" deny science, genetics, environment, biology or psychology necessarily determine man's "moral responsibility," but they proclaim it's God that DECREES such things, and man's will is in absolute bondage to that predestined plan.
Perhaps since one is "spiritual determinism" decreed by God, while the other is some form of "natural determinism" determined by genetics or other like factors, that makes the "spiritual determinism" superior.
Determinism, however, makes humans puppets in a great play, robots programmed to do what they are designed to do, nothing more. Certainly, if man remains in the state in which he was born, he faces a less than positive outcome, not to mention eternity.
However, I don't look at Divine intervention as something that merely changes the track we are on due to a predetermined plan. It's more like God busts up the tracks, replaces our wheels, raises us up and says, "run child! Fly!"
Determinism, even in its finest sense, is still mere bondage. The purpose of God in salvation is for His Glory and for our Freedom. That is what is "determined" for us.
JDale