How to prevent multiple user accounts with the same meta field?

You can use the add_post_meta and update_post_meta filters to accomplish this. If you return anything other than null in these filters the post meta will not be saved.

add_filter('add_post_metadata', 'check_metadata', 10, 5);

function check_metadata($check, $object_id, $meta_key, $meta_value, $prev_value){

/*** Check if the metadata exists via sql ***/
    if($exists) {
         /*** Notify you or something ***/
         return true;
     else {
         return;
     }
}