Switching between skyboxes

You've done a very little mistake, but this is relevant!!! Look at the double "=" in the following statement:

    else
    {
       RenderSettings.skybox == sky;
    }

Replace with:

    else
    {
       RenderSettings.skybox = sky;
    }

Double "=" is for a comparison, single "=" is for an assignment. But I think it was just a copy-&-paste error, since I see that you've understood this logic from the other lines.

EDIT: I also see that your code is inside an Update function, and it's executed every frame. Two problems about this: 1) it's computationally expensive for an operation of skybox changing 2) it's useless, because you couldn't have the time to see the changes, unless the same range of values is generated for a long time. Try this:

 var stars: Material;
 var sky: Material;
 
 RenderSettings.skybox = stars;
 
 function Start()  {
 
    while (true)
    {
       if ( Random.value > 0.5 )
       {
          if (RenderSettings.skybox == sky) 
          {
             RenderSettings.skybox = stars; 
          }
          else
          {
             RenderSettings.skybox = sky;
          }
       }  
    yield WaitForSeconds(1); //adjust the time between the possible change.
    }
 }