I don’t have enough information about your setup to answer correctly. Regardless of Rigidbody settings, your Mover could move in any direction, meaning you have to mind the z within that script as well.
Post your Movement script and we’ll have a look.
If your game world is along the 0 Z axis, i guess something like this could work on your player;
void Update ()
{
Vector3 lockedZpos = transform.position;
lockedZpos.z = 0;
transform.position = lockedZpos ;
}