None of the engines supports this except if your characters are completely physics driven.
Kinematic bodies such as characters are not driven by physics but animations or kinematic movement - manually calculation position of the character in the code. What happens is your character can’t be effected by physics and when it collided with something, PhysX will try to push colliding objects apart, but as your character can’t be pushed back only the other object I’ll be pushed.
What is normally done to solve this is a sweep test of character capsule along his movement path, to check if it will collide with something if he continues to move in his direction. I don’t remember having such issue with FPS template. Which template are you using for your character?
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