3rd person controller- remove smooth rotation

I am attempting to turn the third person controller in the standard assets into a sidescroller controller. So far, I was able to restrict it to where you can only move left and right. My problem here is my character still has the smooth rotation when turning around, and I would like to remove this because, well, it doesn’t fit in with the game.
I have tried removing this line from the third person controller script:

moveDirection = Vector3.RotateTowards(moveDirection, targetDirection, rotateSpeed * Mathf.Deg2Rad * Time.deltaTime, 1000);

While this does remove the smooth rotation like I wanted, facing the opposite direction is delayed a little while moving when it would normally be smoothly rotating.
How can I edit this line or change the third person controller script to remove the smooth rotation but still have my character turn around like usual?

Vector3.RotateTowards is just rotating the moveDirection vector towards the targetDirection, but limit the maximum rotation allowed for this frame with the third parameter (rotateSpeed * Mathf.Deg2Rad * Time.deltaTime) of the function.

If you don’t want any smoothing effect, simply apply directly the targetDirection to moveDirection

moveDirection = targetDirection;