remove rel=next on home page but not others

Here is the answer:

function bg_disable_front_page_wpseo_next_rel_link( $link ) {
    if ( is_front_page() ) {
        return false;
    }

    return $link;
}
add_filter( 'wpseo_next_rel_link', 'bg_disable_front_page_wpseo_next_rel_link' );

You have to return the $link, if you return nothing it will disable it for every single page…