Mouse look script with no world up axis behaves weirdly

So i have a mouse look script for a space game, where the world doesn’t have an ‘up’ direction. It is quite hard to explain my problem, i will try to visualize it.

As you can see, the view doesn’t get back to normal but also rotates by a bit.
What is the problem? The line that does everything:

transform.localRotation *= Quaternion.Euler(-GetMouseY(), GetMouseX(), 0);

The GetMouse() functions are just Input.GetAxis("Mouse X/Y")

If I understand correctly, you are asking why applying only X and Y rotations are resulting in a net rotation in the Z axis after a while.
When you rotate a rotated object it rotates it based off of its local rotation. Imagine in your mind that you rotate an object on just on the X axis by 40 degrees so that its now looking down a bit. Then rotate it from this position on its Y axis 10 degrees to its left. Then rotate it back 40 degrees in its X axis the other way. (Rot x by 40, rot y by 10, rot x by -40). This does NOT result in a net rotation of 10 degrees in the Y axis after all is said and done. That is because the rotations are being applied locally, but since the local rotation has changed due to the y rotation, the are not the same net rotation and therefore do not cancel each other out. On top of that, even though you only applied local X and Y rotations, you will notice that you get a small net rotation in the Z axis when all is said and done.
Hopefully that helped you understand whats happening, but if not don’t worry because there is a simple fix. Instead of applying small delta rotations every frame to your rotated object, just keep track of a TOTAL rotation and apply it completely every frame. Something like this:

private Vector3 localRot;

void Update(){
    localRot += new Vector3(MouseY, MouseX, 0);
    transform.localRotation = Quaternion.Euler(localRot);

Now instead of applying rotations on top of rotations, you just have 1 rotation that you are applying which ensures that no net Z rotation is introduced.