Show media-uploads to all users

The plugin you mentioned is only reportedly tested up to WordPress version 3.6.1.

I would not (in general) recommend abandoned plugins, because they might impose security risks.

Additionally it uses PHP4 class constructors, that might soon be deprecated and it calls non static methods in a static way.

If you remove the plugin, you should be able to use your code snippet:

add_action( 'admin_init', 'mathiregister_allow_uploads' );

function mathiregister_allow_uploads() {
    $contributor = get_role( 'contributor' );
    $contributor->add_cap('upload_files');
}

to allow contributors to get access to the media library and upload files.

Remember to prefix your filter callbacks, to avoid name collisions.

ps: Skimming through the plugin code, you might be able to bypass the plugin’s media restrictions by defining:

define( 'SCOPER_ALL_UPLOADS_EDITABLE ', true );

or do it @toscho style:

const SCOPER_ALL_UPLOADS_EDITABLE = true;

in the global scope, for example in your wp-config.php file.

But you should really consider using up-to-date plugins.