Remove the default value
May be something like this (with hook_form_FORM_ID_alter function): 

function MYMODULE_form_views_exposed_form_alter(&amp;$form, &amp;$form_state) {
  // dpm($form);
  if ($form['#id'] == 'MY_EX_FORM_ID') {
    foreach(element_children($form) as $key =&gt; $value) {
      if (isset($form[$key]['#type']) &amp;&amp; $form[$key]['#type'] == 'select') {
        array_shift($form[$key]['#options']);
      }
    }
  }
}


EDIT:

Ok, it seems that better exposed filter doesn't allow to remove default value from radio if settings are default (with default settings, filter -> is one of, BEF Settings -> checkboxes/radio buttons). I realized that in my project radios have been made from checkboxes type (with alter function), that's why in my example it's working fine..

here is a working example:




in hook_form_form_id_alter function:

foreach(element_children($form) as $key =&gt; $value) {
    if (isset($form[$value]['#type']) &amp;&amp; $form[$value]['#type'] == 'select') {

      $options = $form[$value]['#options'];
      $newOptions = array();

      for ($i = 0, $optionsCount = count($options); $i &lt; $optionsCount; $i++) {
        $optionsKey = array_keys($options[$i]-&gt;option);
        $optionsValue = array_values($options[$i]-&gt;option);

        $newOptions[$optionsKey[0]] = $optionsValue[0];
      }

      unset($form[$value]['#multiple']);

      $form[$value]['#type'] = 'radios';
      $form[$value]['#options'] = $newOptions;
      $form[$value]['#theme'] = 'select_as_radios';
    }
  }