Append taxonomy terms as class names in markup?

Differ the output until you have a collection ready.

$terms = get_the_terms( $post->ID, 'teams' );

// create a collection with your default item
$classes = array('person');

foreach ($terms as $term) {

    // add items
    $classes[] = $term->slug;

}

// output all the classes together with a space to separate them.
echo '<div class="' . implode(' ', $classes) . '">';

echo '<div>More markup for each person listing</div>';

EXCLUDING

To ignore adding any item:

if( $term->slug !== 'accounting' ) { $classes[] = $term->slug; }

To remove all bad apples:

$pros = array('A', 'B', 'C');
$cons = array('C');
$best = array_diff($pros, $cons);
print_r ($best); // A, B

In context:

$terms = get_the_terms( $post->ID, 'teams' );

// create a collection with your default item
$classes = array( 'person' );

if ( $terms && ! is_wp_error( $terms ) ) {
    foreach ( $terms as $term ) {
        $classes[] = $term->slug; // add items
    }
}

// remove any specific classes here
$classes = array_diff( $classes, array( 'creative-services' ) );

// output all the classes together with a space to separate them.
echo '<div class="' . implode( ' ', $classes ) . '">';

echo '<div>More markup for each person listing</div>';