Completely Disable Wordpress Comments (add to functions.php)

functions.php

<?php

// Disable support for comments and trackbacks in post types
function df_disable_comments_post_types_support() {
	$post_types = get_post_types();
	foreach ($post_types as $post_type) {
		if(post_type_supports($post_type, 'comments')) {
			remove_post_type_support($post_type, 'comments');
			remove_post_type_support($post_type, 'trackbacks');
		}
	}
}
add_action('admin_init', 'df_disable_comments_post_types_support');

// Close comments on the front-end
function df_disable_comments_status() {
	return false;
}
add_filter('comments_open', 'df_disable_comments_status', 20, 2);
add_filter('pings_open', 'df_disable_comments_status', 20, 2);

// Hide existing comments
function df_disable_comments_hide_existing_comments($comments) {
	$comments = array();
	return $comments;
}
add_filter('comments_array', 'df_disable_comments_hide_existing_comments', 10, 2);

// Remove comments page in menu
function df_disable_comments_admin_menu() {
	remove_menu_page('edit-comments.php');
}
add_action('admin_menu', 'df_disable_comments_admin_menu');

// Redirect any user trying to access comments page
function df_disable_comments_admin_menu_redirect() {
	global $pagenow;
	if ($pagenow === 'edit-comments.php') {
		wp_redirect(admin_url()); exit;
	}
}
add_action('admin_init', 'df_disable_comments_admin_menu_redirect');

// Remove comments metabox from dashboard
function df_disable_comments_dashboard() {
	remove_meta_box('dashboard_recent_comments', 'dashboard', 'normal');
}
add_action('admin_init', 'df_disable_comments_dashboard');

// Remove comments links from admin bar
function df_disable_comments_admin_bar() {
	if (is_admin_bar_showing()) {
		remove_action('admin_bar_menu', 'wp_admin_bar_comments_menu', 60);
	}
}
add_action('init', 'df_disable_comments_admin_bar');

To hide the comment icon in the admin bar.

add_action( 'admin_bar_menu', 'clean_admin_bar', 999 );
function clean_admin_bar( $wp_admin_bar ) {
    $wp_admin_bar->remove_node( 'comments' );
}

It also turns off the rating function in Woocommerce.