How to allow users to view pending posts of a specific custom post type?

You need to make a custom query to display these pending posts. Here is an example using get_posts():

$args = array(
    'post_type' => 'post_type_name',
    'post_status' => 'pending',
    // -1 shows all
    'posts_per_page' => -1,
);

$pending_posts = get_posts( $args );

foreach( $pending_posts as $pending_post ) {
    // post object properties
    $id = $pending_post->ID;
    $title = $pending_post->post_title;
    $content = $pending_post->post_content;

    // output
    echo $id;
    echo $title;
    echo $content;
}

If you need to filter an existing query instead of making a new one (for example, on an archive page), you should use pre_get_posts().