Sort all posts on all archives alphabetically.

alphabetical-archives.php

<?php
/**
 * Alphabetical Archives
 *
 * @package           alphabetical-archives
 * @author            Bernhard Kau
 * @license           GPL-2.0-or-later
 *
 * @wordpress-plugin
 * Plugin Name:       Alphabetical Archives
 * Plugin URI:        https://gist.github.com/2ndkauboy/96e9c11dc36aa40a762032cf7d040fb0
 * Description:       Sort all posts on all archives alphabetically.
 * Version:           1.0.0
 * Requires at least: 5.0
 * Requires PHP:      5.6
 * Author:            Bernhard Kau
 * Author URI:        https://kau-boys.de
 * License:           GPL v2 or later
 * License URI:       https://www.gnu.org/licenses/gpl-2.0.html
 * Text Domain:       alphabetical-archives
 * Domain Path:       /languages
 */

/**
 * Sort all posts on all category archives alphabetically.
 *
 * @param WP_Query $query The query.
 *
 * @return
 */
function aa_sort_all_archives( $query ) {
	// Only sort main query.
	if ( ! $query->is_main_query() ) {
		return;
	}
	// Only sort category archives.
	if ( ! is_category() ) {
		return;
	}

	$query->set( 'order', 'ASC' );
	$query->set( 'orderby', 'post_title' );
}

add_action( 'pre_get_posts', 'aa_sort_all_archives' );

/**
 * Sort all posts on all category archives alphabetically.
 *
 * @param WP_Query $query The query.
 *
 * @return
 */
function aa_sort_alphabetical_archives( $query ) {
	// Only sort main query.
	if ( ! $query->is_main_query() ) {
		return;
	}
	// Only sort category archives.
	if ( ! is_category( 'alphabetical' ) ) {
		return;
	}

	$query->set( 'order', 'ASC' );
	$query->set( 'orderby', 'post_title' );
}
// Comment this hook in (and the other one out) if you only want to order by a specific category slug
#add_action( 'pre_get_posts', 'aa_sort_alphabetical_archives' );