If using get_the_terms, you can just do your if loop once for each taxonomy and then join them after the three loops.
Of course, it would probably be more efficient to use:
wp_get_post_terms( $post_id, $taxonomy, $args );
You could then do something like:
wp_get_post_terms( $post_id, array( 'resource_roles', 'resource_media', 'resource_theme' ) );
Which would pull all of the terms in one query.
To echo them into your class attribute, use the code you use when they are all the same type:
$extra_classes="";
$terms = wp_get_post_terms( $post_id, array('resource_roles','resource_media','resource_theme');
if ( is_wp_error( $terms ) ) {
# Log the error, notify someone, etc.
} else if ( 0 < count( $terms ) ) {
$slugs = array();
foreach ( $terms as $term ) {
$slugs[] = $term->slug;
}
$extra_classes = implode(' ', $slugs);
}
$title = get_the_title();
echo <<<HTML
<div class="color-shape resource-block {$extra_classes}">
<h1>{$title}</h1>
</div>
HTML;