Demonstrates how to allow HTML in Participants Database text fields

pdb-allow-html-text.php

<?php
/**
 * @wordpress-plugin
 * Plugin Name: PDB Allow HTML
 * Description: Installs a filter allowing HTML in Participants Database text fields
 */
add_filter( 'pdb-text_field_output', 'xnau_allow_html_in_text', 10, 2 );
/**
 * allows sanitized HTML in text fields
 *
 * @param string $text the sanitized content
 * @param object $field the current field
 *
 * @return string the field content to display
 */
function xnau_allow_html_in_text( $text, $field )
{
  if ( $field->form_element === 'text-line' ) {
    /*
     * the wp_kses_post function sanitizes the value by only allowing 
     * certain HTML tags
     * see: https://developer.wordpress.org/reference/functions/wp_kses_post/
     */
    $text = wp_kses_post( $field->value );
  }
  return $text;
}

Download this as a zip file, then install as a plugin, using the "add plugin" item in the WP plugins menu.