`DOING_AJAX` check added. Still doesn't work.

fpw_query_tweaks.php

<?php
/* For query modification */
add_action( 'pre_get_posts', 'hai_resources_pre_get_posts' );
function hai_resources_pre_get_posts( $query ) {

	// stop immediately if we're in the admin or not working with the main query
	if( ( is_admin() && ( ! defined( 'DOING_AJAX' ) || ! DOING_AJAX ) ) || !$query->is_main_query() ) {
		return;
	}

	// modify resource library pages to orderby publication date
	if( is_post_type_archive( 'hai_resources' ) || is_tax( 'hai_countries', 'hai_topics' ) ) {
		$query->set( 'orderby', 'meta_val_num' );
		$query->set( 'order', 'ASC' );
		$query->set( 'meta_key', 'hai_publication_date' );
		$query->set( 'meta_type', 'datetime' );
	}

	return $query;
}