This snippet shows how to prevent a taxonomy from being broadcasted / updated / synced.
In this specific example, all WooCommerce product categories are removed from the broadcast, leaving the categories unsynced.
add_action( 'threewp_broadcast_broadcasting_started', 'my_threewp_broadcast_broadcasting_started' );
function my_threewp_broadcast_broadcasting_started( $action )
{
$bcd = $action->broadcasting_data;
// Remove the product categories from the list of taxonomies the parent blog has.
if ( isset( $bcd->parent_blog_taxonomies[ 'product_cat' ] ) )
unset( $bcd->parent_blog_taxonomies[ 'product_cat' ] );
// Remove the product categories from the list of taxonomies the parent post has.
if ( isset( $bcd->parent_post_taxonomies[ 'product_cat' ] ) )
unset( $bcd->parent_post_taxonomies[ 'product_cat' ] );
}