I made a quick character in blender, imported it in unity, put a capsule collider and a rigidbody on it, and now whenever the character hits the terrain where it is uneven, the character starts spinning in all directions. The project file is attached (change the extension to unityproject, I had to change it because it was saying it was an invalid file type).
Then that would be the rigidbody working? Test this by constraining the rotation on the X and Z axis in the rigidbody inspector.
If you use physics-based stuff like addForce and addTorque then yes having the rotations frozen prevent you from turning the model using scripts. But if you use transform.Rotate then probably not. I really havn’t done much physics based stuff, but if I were you I would do a little test. Make a script that just rotates the char on one of those axis in an update, if it doesn’t rotate, then the constraints do affect transforms. But directly transforming a rigidbody ids not good practice. Perhaps you could lower the center of gravity.