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I can get it to work like this:

$connected_conf2pub = new WP_Query( array(
            'relationship' => array(
                'id'   => 'conf2pub',
                'to' => get_the_ID(), // You can pass object ID or full object
            ),
            'nopaging'     => true,
        ) );

        while ( $connected_conf2pub->have_posts() ) : $connected_conf2pub->the_post();
            echo 'Connected Conf: <a href="' . get_permalink($post->ID) . '"><p>' . get_the_title($post->ID) . '</p></a>';
        endwhile;
        wp_reset_postdata();

        $connected_post2pub = new WP_Query( array(
            'relationship' => array(
                'id'   => 'post2pub',
                'to' => get_the_ID(), // You can pass object ID or full object
            ),
            'nopaging'     => true,
        ) );
        while ( $connected_post2pub->have_posts() ) : $connected_post2pub->the_post();
            echo 'Connected Posts: <a href="' . get_permalink($post->ID) . '"><p>' . get_the_title($post->ID) . '</p></a>';
        endwhile;
        wp_reset_postdata();

        $connected_pub2press = new WP_Query( array(
            'relationship' => array(
                'id'   => 'pub_and_press',
                'from' => get_the_ID(), // You can pass object ID or full object
            ),
            'nopaging'     => true,
        ) );
        while ( $connected_pub2press->have_posts() ) : $connected_pub2press->the_post();
           echo 'Connected Press: <a href="' . get_permalink($post->ID) . '"><p>' . get_the_title($post->ID) . '</p></a>';
        endwhile;
        wp_reset_postdata();

But would like to be able to display all the connections as one for design purposes. I don't really need to identify what's what, I just want to display all connections in date order.

I tried this and it still doesn't work :

$my_query = new WP_Query( array(
    'post_type' => array( 'post', 'page', 'conference', 'publication', 'press'),
    'post_status' => array ('future', 'publish'),
    'paged' => $paged,
    'posts_per_page' => 24
) );

MB_Relationships_API::each_connected( array(
    'id'       => 'conf2pub',
    'from'     => $my_query->posts,
    'property' => 'connected_confs',
) );

MB_Relationships_API::each_connected( array(
    'id'       => 'post2pub',
    'from'     => $my_query->posts,
    'property' => 'connected_posts',
) );

MB_Relationships_API::each_connected( array(
    'id'       => 'pub_and_press',
    'from'     => $my_query->posts,
    'property' => 'connected_press_items',
) );

while ( $my_query->have_posts() ) : $my_query->the_post();

    foreach ( $post->connected_confs as $post ) : setup_postdata( $post );
        the_title();
    endforeach;
    wp_reset_postdata();

    foreach ( $post->connected_posts as $post ) : setup_postdata( $post );
        the_title();
    endforeach;
    wp_reset_postdata();

    foreach ( $post->connected_press_items as $post ) : setup_postdata( $post );
        the_title();
    endforeach;

    wp_reset_postdata();
endwhile;

I get a " Invalid argument supplied for foreach() in " error.

I tried that but I get the same thing.