Plugin demonstration of Customize Setting Validation: validates Customizer settings that contain titles to ensure they are not empty, and then blocks saving the Customizer until they are populated. See https://github.com/xwp/wp-customize-setting-validation

customize-validate-entitled-settings.js

/* global wp, _customizeValidateEntitledSettingsExports */
/* exported customizeValidateEntitledSettings */
var customizeValidateEntitledSettings = ( function( $, api, exports ) {

	var self = {
		l10n: {
			empty_title_invalidity: ''
		}
	};

	if ( exports ) {
		$.extend( self, exports );
	}

	/**
	 * Add validation to a control if it is entitled (has a title or is a title).
	 *
	 * @param {wp.customize.Control} setting                   - Control.
	 * @param {wp.customize.Value}   setting.validationMessage - Validation message.
	 * @return {boolean} Whether validation was added.
	 */
	self.addValidationForEntitledSetting = function( setting ) {
		var initialValidate;

		if ( ! self.isEntitledSetting( setting ) ) {
			return false;
		}
		initialValidate = setting.validate;

		/**
		 * Wrap the setting's validate() method to do validation on the value to be sent to the server.
		 *
		 * @param {mixed} newValue   - New value being assigned to the setting.
		 * @returns {*}
		 */
		setting.validate = function( newValue ) {
			var setting = this, title, validationError;

			// Note: if we want to get the old value, just do oldValue = this.get()
			if ( _.isObject( newValue ) ) {
				title = newValue.title;
			} else {
				title = newValue;
			}
			newValue = initialValidate.call( this, newValue );

			if ( '' === jQuery.trim( title ) ) {
				validationError = new api.Notification( 'empty_title_invalidity', { message: self.l10n.empty_title_invalidity } );
				setting.notifications.add( validationError.code, validationError );
			} else {
				setting.notifications.remove( 'empty_title_invalidity' );
			}
			return newValue;
		};

		return true;
	};

	/**
	 * Return whether the setting is entitled (i.e. if it is a title or has a title).
	 *
	 * @param {wp.customize.Setting} setting - Setting.
	 * @returns {boolean}
	 */
	self.isEntitledSetting = function( setting ) {
		return (
			'blogname' === setting.id
		);
	};

	api.bind( 'add', function( setting ) {
		self.addValidationForEntitledSetting( setting );
	} );

	return self;

}( jQuery, wp.customize, _customizeValidateEntitledSettingsExports ) );

customize-validate-entitled-settings.php

<?php
/**
 * Plugin name: Customize Validate Entitled Settings
 * Description: Prevent the site title, nav menu items, and widget instances from being saved without titles. Enforces title case via sanitization. Depends on patch from <a href="https://core.trac.wordpress.org/ticket/34893">#34893</a> plugin.
 * Author: Weston Ruter, XWP.
 * Plugin URL: https://gist.github.com/westonruter/1016332b18ee7946dec3
 * Version: 0.2
 * Author: XWP
 * Author URI: https://xwp.co/
 * License: GPLv2+
 * License URI: http://www.gnu.org/licenses/gpl-2.0.txt
 * Text Domain: customize-validate-entitled-settings
 *
 * Copyright (c) 2016 XWP (https://xwp.co/)
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License, version 2 or, at
 * your discretion, any later version, as published by the Free
 * Software Foundation.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
 */

/**
 * Class Customize_Validate_Entitled_Settings
 */
class Customize_Validate_Entitled_Settings {

	/**
	 * Translated strings
	 *
	 * @var array
	 */
	public $l10n = array();

	/**
	 * Add hooks.
	 */
	public function init() {
		require_once ABSPATH . WPINC . '/class-wp-customize-setting.php';
		if ( ! method_exists( 'WP_Customize_Setting', 'validate' ) ) {
			add_action( 'admin_notices', array( $this, 'show_admin_notice_for_missing_patch' ) );
			return;
		}

		add_action( 'customize_register', array( $this, 'add_filters_for_setting_validation' ), 100 );

		// Prevent performing validation during update-widget request so that form can actually return with a full response.
		// @todo This has only been needed since 4.8 and it seems to only be an issue for the Text widget. More investigation is needed.
		$is_update_widgets_request = ( wp_doing_ajax() && isset( $_REQUEST['action'] ) && 'update-widget' === $_REQUEST['action'] );
		if ( ! $is_update_widgets_request ) {
			add_filter( 'widget_customizer_setting_args', array( $this, 'filter_widget_customizer_setting_args' ), 10, 2 );
		}

		add_action( 'customize_controls_enqueue_scripts', array( $this, 'customize_controls_enqueue_scripts' ) );
		$this->l10n = array(
			'empty_title_invalidity' => __( 'You must supply a title/label.', 'customize-validate-entitled-settings' ),
			'shouting_title_invalidity' => __( 'YOU ARE NOT ALLOWED TO SHOUT.', 'customize-validate-entitled-settings' ),
			'indecisive_title_invalidity' => __( 'Why not avoid questions in titles/labels?', 'customize-validate-entitled-settings' ),
		);
	}

	/**
	 * Show admin notice when patch from #34893 is not applied.
	 */
	public function show_admin_notice_for_missing_patch() {
		?>
		<div class="error">
			<p>The <strong>Customize Validate Entitled Settings</strong> plugin requires the patch from <a href="https://core.trac.wordpress.org/ticket/34893">#34893</a> to be applied.</p>
		</div>
		<?php
	}

	/**
	 * Enqueue scripts.
	 *
	 * @action customize_controls_enqueue_scripts
	 */
	public function customize_controls_enqueue_scripts() {
		$handle = 'customize-validate-entitled-setting';
		$src = plugin_dir_url( __FILE__ ) . 'customize-validate-entitled-settings.js';
		$deps = array( 'customize-controls' );
		wp_enqueue_script( $handle, $src, $deps );

		$exports = array(
			'l10n' => $this->l10n,
		);
		wp_scripts()->add_data( $handle, 'data', sprintf( 'var _customizeValidateEntitledSettingsExports = %s;', wp_json_encode( $exports ) ) );
	}

	/**
	 * Add filters for setting validation.
	 *
	 * @param WP_Customize_Manager $wp_customize Customize manager.
	 */
	public function add_filters_for_setting_validation( $wp_customize ) {
		add_filter( 'customize_sanitize_blogname', array( $this, 'sanitize_title' ) );
		add_filter( 'customize_validate_blogname', array( $this, 'validate_title' ), 10, 3 );

		// Add filters to all nav menu items and widget instances.
		foreach ( $wp_customize->settings() as $setting ) {
			if ( $setting instanceof WP_Customize_Nav_Menu_Item_Setting || $setting instanceof WP_Customize_Post_Setting ) {
				add_filter( "customize_sanitize_{$setting->id}", array( $this, 'sanitize_array_containing_title' ) );
				add_filter( "customize_validate_{$setting->id}", array( $this, 'validate_array_containing_title' ), 10, 3 );
			}
		}
	}

	/**
	 * Side-load filters for sanitizing and validating widget settings.
	 *
	 * This method of adding filters is somewhat hacky. It is necessary due to
	 * incoming dirty settings being previewed immediately after the settings
	 * dynamic widget settings are created.
	 *
	 * In the future a widget should handle this via implementing `WP_JS_Widget::validate()`.
	 *
	 * @link https://github.com/xwp/wp-js-widgets/pull/8/files#diff-42d2172baac53c364a4b33471b86c9d5R275
	 *
	 * @see WP_Customize_Widgets::register_settings()
	 *
	 * @param array  $args Setting args.
	 * @param string $id   Setting ID.
	 * @return array Args unmodified.
	 */
	public function filter_widget_customizer_setting_args( $args, $id ) {
		$prefix = 'widget_';
		if ( substr( $id, 0, strlen( $prefix ) ) === $prefix ) {
			/*
			 * Note that the sanitize filter needs to be higher than 10 which is
			 * the priority at which a JS-sanitized encoded-serialized instance
			 * is converted to its internal array representation. This only
			 * applies to legacy widgets that do not extend WP_JS_Widget.
			 * The priority of 10 is specified in `WP_Customize_Setting::__construct()`
			 * where the filter for `customize_sanitize_{$id}` is added for the
			 * setting's `sanitize_callback`.
			 */
			$priority = 20;

			add_filter( "customize_sanitize_{$id}", array( $this, 'sanitize_array_containing_title' ), $priority, 2 );
			add_filter( "customize_validate_{$id}", array( $this, 'validate_array_containing_title' ), $priority, 3 );
		}
		return $args;
	}

	/**
	 * Validate a title field after sanitizing with ucwords() for demonstration purposes.
	 *
	 * @param string $value Title.
	 * @return string       String if valid, error if not.
	 */
	public function sanitize_title( $value ) {
		$value = sanitize_text_field( $value );
		$value = ucwords( $value );
		return $value;
	}

	/**
	 * Validate a (sanitized) title to not be empty.
	 *
	 * @param WP_Error $validity Validity.
	 * @param string   $value    Value, normally pre-sanitized.
	 * @param string   $setting  Setting.
	 * @return WP_Error
	 */
	public function validate_title( $validity, $value, $setting ) {
		$data = array();
		if ( $setting instanceof WP_Customize_Post_Setting ) {
			$data['setting_property'] = 'post_title';
		}
		if ( '' === $value ) {
			$validity->add( 'empty_title_invalidity', $this->l10n['empty_title_invalidity'], $data );
		}
		if ( false !== strpos( $value, '!' ) ) {
			$validity->add( 'shouting_title_invalidity', $this->l10n['shouting_title_invalidity'], $data );
		}
		if ( false !== strpos( $value, '?' ) ) {
			$validity->add( 'indecisive_title_invalidity', $this->l10n['indecisive_title_invalidity'], $data );
		}
		return $validity;
	}

	/**
	 * Sanitize an array containing a title property.
	 *
	 * @param array $data {
	 *     Array containing a title.
	 *
	 *     @type string [$title] Title.
	 * }
	 *
	 * @return array|WP_Error Returns sanitized array if title is valid, WP_Error otherwise.
	 */
	public function sanitize_array_containing_title( $data ) {
		if ( is_array( $data ) ) {
			if ( array_key_exists( 'title', $data ) ) {
				$data['title'] = $this->sanitize_title( $data['title'] );
			} elseif ( array_key_exists( 'post_title', $data ) ) {
				$data['post_title'] = $this->sanitize_title( $data['post_title'] );
			}
		}
		return $data;
	}

	/**
	 * Validate an array containing a title property.
	 *
	 * @param null|true|WP_Error   $validity Validity.
	 * @param array                $data {
	 *     Array containing a title.
	 *
	 *     @type string [$title] Title.
	 * }
	 * @param WP_Customize_Setting $setting  Setting.
	 *
	 * @return array|WP_Error Returns sanitized array if title is valid, WP_Error otherwise.
	 */
	public function validate_array_containing_title( $validity, $data, $setting = null ) {
		if ( is_array( $data ) ) {
			if ( $setting instanceof WP_Customize_Nav_Menu_Item_Setting ) {
				$can_use_original_title = ( ! empty( $data['type'] ) && 'post_type_archive' === $data['type'] || ! empty( $data['object_id'] ) );
				if ( empty( $data['title'] ) && ! $can_use_original_title ) {
					$validity = $this->validate_title( $validity, '', $setting );
				}
			} elseif ( array_key_exists( 'title', $data ) ) {
				$validity = $this->validate_title( $validity, $data['title'], $setting );
			} elseif ( $setting instanceof WP_Customize_Post_Setting && 'trash' !== $data['post_status'] ) {
				$validity = $this->validate_title( $validity, $data['post_title'], $setting );
			}
		}
		return $validity;
	}

	/**
	 * Filter a widget's settings before saving.
	 *
	 * Returning false will effectively short-circuit the widget's ability
	 * to update settings.
	 *
	 * This was added in init() via `add_filter( 'widget_update_callback', array( $this, 'sanitize_and_validate_widget_instance' ), 10, 4 );`
	 * It was disabled, however, because it provides a poor experience in that it
	 * just blocks a form edit from sticking and it doesn't allow any invalid
	 * setting values to be submitted, and thus no opportunity for rejection and
	 * displaying of the invalidity message.
	 *
	 * @param array $instance     The current widget instance's settings.
	 * @param array $new_instance Array of new widget settings.
	 * @param array $old_instance Array of old widget settings.
	 * @return array|false
	 */
	public function sanitize_and_validate_widget_instance( $instance, $new_instance, $old_instance ) {
		unset( $new_instance, $old_instance );
		if ( ! isset( $instance['title'] ) ) {
			$instance['title'] = '';
		}
		$instance = $this->sanitize_array_containing_title( $instance );
		$validity = $this->validate_array_containing_title( new WP_Error(), $instance );
		if ( ! empty( $validity->errors ) ) {
			return false;
		}
		return $instance;
	}
}

$customize_validate_entitled_settings_plugin = new Customize_Validate_Entitled_Settings();
add_action( 'plugins_loaded', array( $customize_validate_entitled_settings_plugin, 'init' ) );