Texture2D looks blank in after using ReadPixels, but it's not when saved

I am trying to replace a texture in a GameObject with a custom one. The new texture looks blank, but if I save it to disk and load that image into the GameObject, then it works fine. I want to avoid that saving step, because I'm not sure I'm allowed to do that in mobile platforms...

Here's what I did:

• I created a class that it does not inherit from MonoBehaviour.

• The class has a Texture2D member _texture.

• The class has a method that uses a custom shader to draw something on a RenderTexture.

• I use ReadPixels to copy the contents of this RenderTexture to _texture.

The method does something like this:

 public void myFunction() {
    WWW _texLoader = new WWW("file://"+Application.dataPath+"sometexture.png");
    Texture2D source = new Texture2D(W, H, TextureFormat.ARGB32, false);
    _texLoader.LoadImageIntoTexture(source);
    RenderTexture rTexture = RenderTexture.GetTemporary(W, H, 0, RenderTextureFormat.ARGB32 );
    Material material = new Material(Shader.Find("MyMaterial"));
    Graphics.Blit(source, rTexture, material);
    // activate rTexture as current render target, so ReadPixels reads from it
    RenderTexture.active = rTexture ;
    Rect sourceRect = new Rect(0,0,W,H);
    _texture.ReadPixels(sourceRect, 0, 0);
    // go back to main context
    RenderTexture.active = null ;
    RenderTexture.ReleaseTemporary(rTexture);  
 }
 public Texture2D GetTexture() {
    return _texture;
 }

After that, the image is set somewhere else to a GameObject using GetTexture(), but it looks blank. However, if I apply the function below, then it works.

 public Texture2D GetAnotherTexture() {
     Texture2D texture = new Texture2D(W, H, TextureFormat.ARGB32, false);
     texture.LoadImage(File.ReadAllBytes(GetMyPath()));
     return texture ;
 }

I have tried the things below, but nothing seems to work:

• Making _texture static

• Waiting 1 frame before setting the texture to the GameObject

Do I have to WaitForEndOfFrame()? I am writing to my own RenderTarget with RenderTexture.active, right? So I guess it should work (it actually works, since the saved image is fine...) I guess it has something to do with the state of the Texture2D image, but I can't find any help in the documentation. Any suggestions? Thanks in advance.