Simple Parallax

// Script 1

using UnityEngine;
using System.Collections;

public class ParallaxOption : MonoBehaviour {

    public bool moveParallax;

    [SerializeField]
    [HideInInspector]
    private Vector3 storedPosition;

    public void SavePosition() {
        storedPosition = transform.position;
    }

    public void RestorePosition() {
        transform.position = storedPosition;
    }
}

// Script 2

using UnityEngine;
using System.Collections;

[ExecuteInEditMode]
public class ParallaxLayer : MonoBehaviour {
    public float speedX;
    public float speedY;
    public bool moveInOppositeDirection;

    private Transform cameraTransform;
    private Vector3 previousCameraPosition;
    private bool previousMoveParallax;
    private ParallaxOption options;

    void OnEnable() {
        GameObject gameCamera = GameObject.Find("Main Camera");
        options = gameCamera.GetComponent<ParallaxOption>();
        cameraTransform = gameCamera.transform;
        previousCameraPosition = cameraTransform.position;
    }

    void Update () {
        if(options.moveParallax && !previousMoveParallax)
            previousCameraPosition = cameraTransform.position;

        previousMoveParallax = options.moveParallax;

        if(!Application.isPlaying && !options.moveParallax)
            return;

        Vector3 distance = cameraTransform.position - previousCameraPosition;
        float direction = (moveInOppositeDirection) ? -1f : 1f;
        transform.position += Vector3.Scale(distance, new Vector3(speedX, speedY)) * direction;

        previousCameraPosition = cameraTransform.position;
    }
}