This gist works when there are already bp_member_types. It adds tab for each member type which has_directory and at least one active user of this bp_member_type

bp_member_type_directory.php

////-----

// 2. display members type tabs
function ls_display_members_directory_tabs() {
    $member_types = bp_get_member_types( array(), 'objects' );
 
    // Loop in member types to build the tabs
    foreach ( $member_types as $member_type ) : 
        
  if ($member_type->has_directory) {
      if (ls_count_member_types( $member_type->name ) >0) {
        ?>
 
    <li id="members-<?php echo esc_attr( $member_type->name ) ;?>">
        <a href="<?php bp_member_type_directory_permalink($member_type->name); ?>"><?php printf( '%s <span>%d</span>', $member_type->labels['name'],
              ls_count_member_types( $member_type->name ) 
                ); ?></a>
    </li>
 
    <?php
      }
  }
    endforeach;
}
// group main nav bar
add_action( 'bp_members_directory_member_types', 'ls_display_members_directory_tabs' );



//// 3. get the member type count
function ls_count_member_types( $member_type = '', $taxonomy = 'bp_member_type' ) {
    global $wpdb;
    $member_types = bp_get_member_types( array(), 'objects' );
 
    if ( empty( $member_type ) || empty( $member_types[ $member_type ] ) ) {
        return false;
    }
 
    $count_types = wp_cache_get( 'bp_count_member_types', 'bp_count_member_types' );
 
    if ( ! $count_types ) {
        if ( ! bp_is_root_blog() ) {
            switch_to_blog( bp_get_root_blog_id() );
        }
 
        $sql=array(
            'select' => "SELECT count({$wpdb->users}.ID) as count, {$wpdb->terms}.slug  FROM {$wpdb->users}",
            'on'     => " INNER JOIN {$wpdb->term_relationships} on {$wpdb->users}.ID={$wpdb->term_relationships}.object_id ".
                       " INNER JOIN {$wpdb->term_taxonomy} on {$wpdb->term_relationships}.term_taxonomy_id={$wpdb->term_taxonomy}.term_taxonomy_id ".
                       " INNER JOIN {$wpdb->terms} on {$wpdb->terms}.term_id={$wpdb->term_taxonomy}.term_id ",
            'where1'  => $wpdb->prepare( "WHERE {$wpdb->term_taxonomy}.taxonomy = %s", $taxonomy ),
            'where2'  => " AND {$wpdb->users}.user_status = 0" ,
            'group by'=> " GROUP BY {$wpdb->terms}.slug "
                 );


        $count_types = $wpdb->get_results( join( ' ', $sql ) );
        wp_cache_set( 'bp_count_member_types', $count_types, 'bp_count_member_types' );
 
        restore_current_blog();
    }
 
    $type_count = wp_filter_object_list( $count_types, array( 'slug' => $member_type ), 'and', 'count' );
    $type_count = array_values( $type_count );
 
    if ( empty( $type_count ) ) {
        return 0;
    }
 
    return (int) $type_count[0];
}
//// 4. display member type tab content
function ls_set_has_members_type_arg( $args = array() ) {
    // Get member types to check scope
      $member_types = bp_get_member_types( array(), 'objects' );
      
      // Set the group type arg if scope match one of the registered group type
    if ( ! empty( $args['scope'] ) && ! empty( $member_types[ $args['scope'] ] ) ) {
        $args['member_type'] = $args['scope'];
        
    }
    
    return $args;
} 
add_filter( 'bp_before_has_members_parse_args', 'ls_set_has_members_type_arg', 10, 2 );

//// 5. display member type on directory
function ls_member_directory_show_member_type( $member_id = NULL )  {
    if ( empty( $member_id ) ) {
        $member_id = bp_get_member_user_id();
    }
 
    // Members directory.
    if( bp_is_active( 'members' ) && bp_is_members_directory() ) {
        // Get member types to check scope
        $member_types =  bp_get_member_type( $member_id ,false );
        if ($member_types) {
            foreach ( $member_types as $type ) {
                $obj =(array)bp_get_member_type_object( $type );

                 // Member type name/description.
                printf( '<div class="dir-desc-'.$obj['labels']['singular_name'].'" ><span class="dir-desc-span-name">%1$s</span>.', $obj['labels']['singular_name'].'</div>' );
            }
        }
    }
}
add_action( 'bp_directory_members_item', 'ls_member_directory_show_member_type' );