Add a relationship to logged in user, not content author, on content view?
There is no way to accomplish this via UI. At least not if the User field may contain multiple values. 

In the example below 'field_test' is a List(text) field w/ select widget (unlimited values allowed for user account). When the same field is added to Content type - I set it to allow for single values.

The code will take in consideration multiple values from User field and add WHERE  clause to the View that shows all nodes of a Content type.

WHERE clause filters out all nodes that have 'field_test' set to anything other than what currently logged in user has set in 'field_test' on their own account.

/**
* Implements hook_views_query_alter().
*/
function MYMODULE_views_query_alter(&amp;$view, &amp;$query) {
  // 'test_related_field' -&gt; view's machine_name
  if ($view-&gt;name == 'test_related_field') {
    global $user;
    $user = user_load($user-&gt;uid);

    // 'field_test' -&gt; field that is shared between user accounts ans content type
    $user_field = field_get_items('user', $user, 'field_test');
    if($user_field) {
        $query-&gt;ensure_table("field_data_field_test");
        // create query that processes multiple values of User 'field_test'
        $db_or = db_or(); 
        foreach ($user_field as $item){
            $db_or-&gt;condition('field_data_field_test.field_test_value', $item, 'IN'); 
        }
        $query-&gt;add_where('test_field_group', $db_or);
    }
    // use dpm() to see added WHERE clause
    //dpm($query);
  }
}


UPDATE:
If User field and Content Type field are allowed to have only single values then you can use UI for filtering view's results. 


add shared field as Contextual Filter
Provide Default value for the field -> select PHP Code
enter the following code in the box


global $user;
$user_fields = user_load($user-&gt;uid);
$test_field = $user_fields-&gt;field_test['und'][0]['value'];
return $test_field;