Mouse movement broken after animation

I have a player gameobject with this structure: Player - Character controller, First person controller script, rigidbody FirstPersonCharacter - Camera

I made a wake up animation, animating the camera (the animator is on the camera too), and after the animation is finished I can move my player and rotate horizontally, but not vertically.

I tried disabling the animator after the animation is finished and the mouse movement now works completely. Setting the animator to apply root motion works but breaks the animation (doesn't look like it's supposed to).

Is there a way to fix this?