Add Api_channel_fields back to the entries parser. Update the replace() methods in the following two core files: system/expressionengine/libraries/channel_entries_parser/components/Custom_field.php system/expressionengine/libraries/channel_entries_parser/components/Custom_field_pair.php

Custom_field.php

<?php

public function replace($tagdata, EE_Channel_data_parser $obj, $ft_api)
{
    $tag = $obj->tag();
    $data = $obj->row();
    $prefix = $obj->prefix();

    $site_id = $data['site_id'];
    $cfields = $obj->channel()->cfields;
    $rfields = $obj->channel()->rfields;

    $rfields = isset($rfields[$site_id]) ? $rfields[$site_id] : array();
    $cfields = isset($cfields[$site_id]) ? $cfields[$site_id] : array();

    $cfields = array_diff_key($cfields, $rfields);

    if (empty($cfields))
    {
        return $tagdata;
    }

    $unprefixed_tag = preg_replace('/^'.$prefix.'/', '', $tag);
    $field_name     = substr($unprefixed_tag.' ', 0, strpos($unprefixed_tag.' ', ' '));
    $param_string   = substr($unprefixed_tag.' ', strlen($field_name));

    $modifier = '';
    $modifier_loc = strpos($field_name, ':');

    if ($modifier_loc !== FALSE)
    {
        $modifier = substr($field_name, $modifier_loc + 1);
        $field_name = substr($field_name, 0, $modifier_loc);
    }

    if (isset($cfields[$field_name]))
    {
        $entry = '';
        $field_id = $cfields[$field_name];

        if (isset($data['field_id_'.$field_id]) && $data['field_id_'.$field_id] != '')
        {
            $params = array();
            $parse_fnc = ($modifier) ? 'replace_'.$modifier : 'replace_tag';

            if ($param_string)
            {
                $params = ee()->functions->assign_parameters($param_string);
            }

            $obj = $ft_api->setup_handler($field_id, TRUE);

            if ($obj)
            {
                /*
                $_ft_path = $ft_api->ft_paths[$ft_api->field_type];
                ee()->load->add_package_path($_ft_path, FALSE);

                $obj->_init(array('row' => $data));

                $data = $obj->pre_process($data['field_id_'.$field_id]);

                if (method_exists($obj, $parse_fnc))
                {
                    $entry = $obj->$parse_fnc($data, $params, FALSE);
                }
                elseif (method_exists($obj, 'replace_tag_catchall'))
                {
                    $entry = $obj->replace_tag_catchall($data, $params, FALSE, $modifier);
                }
                */
                
                ee()->load->library('api');
                ee()->api->instantiate('channel_fields');

                ee()->api_channel_fields->apply('_init', array(array('row' => $data)));
                $data = ee()->api_channel_fields->apply('pre_process', array($data['field_id_'.$field_id]));
                    
                if (ee()->api_channel_fields->check_method_exists($parse_fnc))
                {
                    $entry = ee()->api_channel_fields->apply($parse_fnc, array($data, $params, FALSE));
                }
                elseif (ee()->api_channel_fields->check_method_exists($parse_fnc_catchall))
                {
                    $entry = ee()->api_channel_fields->apply($parse_fnc_catchall, array($data, $params, FALSE, $modifier));
                }
            }
            else
            {
                // Couldn't find a fieldtype
                $entry = ee()->typography->parse_type(
                    ee()->functions->encode_ee_tags($data['field_id_'.$field_id]),
                    array(
                        'text_format'   => $data['field_ft_'.$field_id],
                        'html_format'   => $data['channel_html_formatting'],
                        'auto_links'    => $data['channel_auto_link_urls'],
                        'allow_img_url' => $data['channel_allow_img_urls']
                    )
                );
            }

            // prevent accidental parsing of other channel variables in custom field data
            if (strpos($entry, '{') !== FALSE)
            {
                $entry = str_replace(
                    array('{', '}'),
                    array(unique_marker('channel_bracket_open'), unique_marker('channel_bracket_close')),
                    $entry
                );
            }

            $tagdata = str_replace(LD.$tag.RD, $entry, $tagdata);
        }

        $tagdata = str_replace(LD.$tag.RD, '', $tagdata);
    }

    return $tagdata;
}

Custom_field_pair.php

<?php

public function replace($tagdata, EE_Channel_data_parser $obj, $pfield_chunks)
{
    $data = $obj->row();
    $prefix = $obj->prefix();

    $site_id = $data['site_id'];

    $cfields = $obj->channel()->cfields;
    $cfields = isset($cfields[$site_id]) ? $cfields[$site_id] : array();

    if (empty($cfields) OR ! isset($pfield_chunks[$site_id]))
    {
        return $tagdata;
    }

    $pfield_chunk = $pfield_chunks[$site_id];
    $ft_api = ee()->api_channel_fields;

    foreach ($pfield_chunk as $tag_name => $chunks)
    {
        $field_name = preg_replace('/^'.$prefix.'/', '', $tag_name);
        $field_name = substr($field_name, strpos($field_name, ' '));
        $field_id = $cfields[$field_name];

        $obj = $ft_api->setup_handler($field_id, TRUE);

        if ($obj)
        {
            /*
            $_ft_path = $ft_api->ft_paths[$ft_api->field_type];
            ee()->load->add_package_path($_ft_path, FALSE);

            $obj->_init(array('row' => $data));
            $pre_processed = $obj->pre_process($data['field_id_'.$field_id]);
            */
        
            ee()->load->library('api');
            ee()->api->instantiate('channel_fields');

            ee()->api_channel_fields->apply('_init', array(array('row' => $data)));
            $pre_processed = ee()->api_channel_fields->apply('pre_process', array($data['field_id_'.$field_id]));
            
            foreach($chunks as $chk_data)
            {
                list($modifier, $content, $params, $chunk) = $chk_data;

                $tpl_chunk = '';
                // Set up parse function name based on whether or not
                // we have a modifier
                $parse_fnc = ($modifier) ? 'replace_'.$modifier : 'replace_tag';

                /*
                if (method_exists($obj, $parse_fnc))
                {
                    $tpl_chunk = $obj->$parse_fnc($pre_processed, $params, $content);
                }
                // Go to catchall and include modifier
                elseif (method_exists($obj, 'replace_tag_catchall') AND $modifier !== '')
                {
                    $tpl_chunk = $obj->replace_tag_catchall($pre_processed, $params, $content, $modifier);
                }
                */
            
                if (ee()->api_channel_fields->check_method_exists($parse_fnc))
                {
                    $tpl_chunk = ee()->api_channel_fields->apply($parse_fnc, array($pre_processed, $params, $content));
                }
                elseif (ee()->api_channel_fields->check_method_exists('replace_tag_catchall'))
                {
                    $tpl_chunk = ee()->api_channel_fields->apply($parse_fnc_catchall, array($data, $params, $content, $modifier));
                }

                $tagdata = str_replace($chunk, $tpl_chunk, $tagdata);
            }
        }
    }

    return $tagdata;
}