Making some Views Exposed Filters auto-submit but not others
Gonna add my 2 cents too on the topic, since I recently did my reading-into this topic (autosubmit for exposed filters).

Related:

This answer here answers a very similar problem => https://drupal.stackexchange.com/a/198274/57183.

Usefull things to know

The most important piece of relevant documentation lies inside the ctools/js/auto-submit.js file of CTools, at the top of that file. 

Form API programming

Following that documentation, you should use the FAPI to programmatically do one of the following: 


Exclude the specific filters that you don't want to be trigger an autosubmit (if you have autosubmit active, like in your case):


  If you want to exclude a field from the ctool-auto-submit-full-form
  auto submission, add the class ctools-auto-submit-exclude to the form
  element. With FAPI, add:
  
  '#attributes' => array('class' =>
  array('ctools-auto-submit-exclude')),

Include the filters that you want to trigger an autosubmit (if you have autosubmit deactivated, not your case)


  On gadgets you want to auto-submit when changed, add the
  ctools-auto-submit class. With FAPI, add:
  
  '#attributes' => array('class' => array('ctools-auto-submit')),



After that, you already have the functionality you need.

Example to the Example

Following your example here is some example code (with inline comments):

function somemodule_form_views_exposed_form_alter(&amp;$form, &amp;$form_state, $form_id) {

  // Assumption: Auto-submit is activated via the Views/BEF configuration for all filters
  // Therefore, we will exclude "the text boxes and some of the radio buttons..."

  $exposed_filters_to_deactivate = array(
    'full_text_search', // a text field
    'field_categories', // a radio button
  );

  foreach($exposed_filters_to_deactivate as $exposed_filter_name) {

    // This will disable auto-submitting the form for our filter element
    $form[$exposed_filter_name]['#attributes'] = array('class' =&gt; array('ctools-auto-submit-exclude'));

  }

}


This should do it, now the exposed filters full_text_search' and 'field_categories' will not trigger an autosubmit event, all other filters will.

Hope this helps!

Addendum (follow-up question):

To get specific checkboxes from a BEF-checkbox group to trigger a form submit, you need to do the following:

Modify you form_alter implementation:  

function somemodule_form_views_exposed_form_alter(&amp;$form, &amp;$form_state, $form_id) {

  // Assumption: Auto-submit is activated via the Views/BEF configuration for all filters
  // Therefore, we will exclude "the text boxes and some of the radio buttons..."

  $exposed_filters_to_deactivate = array(
    'full_text_search', // a text field
    'field_categories', // a radio button
    'field_areas_of_interest_checkbox', // a BEF-checkboxes widget
  );

  foreach($exposed_filters_to_deactivate as $exposed_filter_name) {

    // This will disable auto-submitting the form for our filter element
    $form[$exposed_filter_name]['#attributes'] = array('class' =&gt; array('ctools-auto-submit-exclude'));

  }

  // This is the name of the select values and their target url
  $bef_checkboxes_autosubmit = array(
    '#area_of_interest_checkbox_1',
    '#area_of_interest_checkbox_3',
  );

  // This will attach a javascript to the checkboxes element
  $form['field_areas_of_interest_checkbox']['#attached']['js'][] = drupal_get_path('module', 'somemodule') . '/somemodule.js';
  $form['field_areas_of_interest_checkbox']['#attached']['js'][] = array(
    'data' =&gt; array(
      'bef_checkboxes_autosubmit' =&gt; array(
        'form_id' =&gt; $form['#id'],
        'checkboxes_ids' =&gt; $bef_checkboxes_autosubmit,
      )
    ),
    'type' =&gt; 'setting'
  );
}


Now, you also need a javascript file (somemodule.js) that will look sth like this:

(function($){

Drupal.behaviors.BEFCustomRedirect = {
  attach: function(context, settings) {
    $(settings.bef_checkboxes_autosubmit.checkboxes_ids).each( function( idx ) {
      $('.ctools-auto-submit-exclude.form-checkboxes input' + this).change(function() {
        $('#' + settings.bef_checkboxes_autosubmit.form_id).submit();
      });
    });
  }
}

})(jQuery);