gistfile1.diff

Index: domain_mapping.php
===================================================================
--- domain_mapping.php  (revision 646767)
+++ domain_mapping.php	(working copy)
@@ -519,6 +519,10 @@
 }
 
 function domain_mapping_siteurl( $setting ) {
+	// Don't redirect customizer requests
+	if ( isset( $_SERVER['HTTP_REFERER'] ) && false !== strpos( $_SERVER['HTTP_REFERER'], 'wp-admin/customize.php' ) )
+		return $setting;
+
 	global $wpdb, $current_blog;
 
 	// To reduce the number of database queries, save the results the first time we encounter each blog ID.