The problem is due to the URL having a series of redirects that includes going from HTTPS to HTTP, which is not secure.

You can see the redirects that are performed by loading the original URL in a browser and checking the network request tab in the developer console:

You can confirm that this is causing an error by adding a handler to the Image control's ImageFailed event:

Image control:

<Image Source="http://cdn-www.airliners.net/aviation-photos/photos/7/0/1/1892107.jpg" 
        ImageFailed="Image_ImageFailed" />

Event handler:

private void Image_ImageFailed(object sender, ExceptionRoutedEventArgs e)
{
    Debug.WriteLine(e.ErrorException.Message);
}

This will result in the following error message being printed to the debug output:

The remote server returned an error: (301) Moved Permanently.

Why does this only happen in .NET Core?

Image uses HttpWebRequest underneath to resolve URL sources. With .NET Core, the HttpWebRequest behavior was intentionally changed to not allow following HTTPS -> HTTP redirects because it is a security risk. You can check out this issue for details, especially this post from David Shulman:

Yes, this is by-design in .NET Core. This is a security-related change to prevent HTTPS -> HTTP redirection which is inherently insecure.