remove other tabs in new wordpress media gallery

If you want to hide the Media Library submenu:

you can do it via the admin_menu action:

function wpse85351_hide_submenus() {
      if(!current_user_can('edit_posts')){
           global $submenu;
           unset($submenu['upload.php'][5]); // hide the Media Library
      }
}
add_action('admin_menu', 'wpse85351_hide_submenus');

If you want to change/remove the Media strings:

you can use the media_view_strings filter:

function wpse85351_media_strings($strings) {
    // only for subscribers:
    if(!current_user_can('edit_posts')){
        // remove "mediaLibraryTitle"
        unset($strings["mediaLibraryTitle"]);
    }
    return $strings;
}
add_filter('media_view_strings','wpse85351_media_strings');

You can use

!current_user_can('edit_posts')

instead of

!current_user_can( 'administrator' ) || !current_user_can( 'editor' ) || !current_user_can( 'contibutor' ) || !current_user_can( 'author' )

to restrict it only to “subscribers”.

Here is the array of all the Media View Strings that you can unset or change to your needs:

Array
(
    [url] => URL
    [addMedia] => Add Media
    [search] => Search
    [select] => Select
    [cancel] => Cancel
    [selected] => %d selected
    [dragInfo] => Drag and drop to reorder images.
    [uploadFilesTitle] => Upload Files
    [uploadImagesTitle] => Upload Images
    [mediaLibraryTitle] => Media Library
    [insertMediaTitle] => Insert Media
    [createNewGallery] => Create a new gallery
    [returnToLibrary] => ← Return to library
    [allMediaItems] => All media items
    [noItemsFound] => No items found.
    [insertIntoPost] => Insert into post
    [uploadedToThisPost] => Uploaded to this post
    [warnDelete] => You are about to permanently delete this item.
  'Cancel' to stop, 'OK' to delete.
    [insertFromUrlTitle] => Insert from URL
    [setFeaturedImageTitle] => Set Featured Image
    [setFeaturedImage] => Set featured image
    [createGalleryTitle] => Create Gallery
    [editGalleryTitle] => Edit Gallery
    [cancelGalleryTitle] => ← Cancel Gallery
    [insertGallery] => Insert gallery
    [updateGallery] => Update gallery
    [addToGallery] => Add to gallery
    [addToGalleryTitle] => Add to Gallery
    [reverseOrder] => Reverse order
)