Do you have a caching server, such as Varnish in front of wordpress? If so, you might be swallowing the cookies that customize.php needs when it tries to display the front page (wordpress_*, wordpress_logged_in_*, wp-settings-1, wp-settings-time-1 to name a few).
I had this problem (because I was removing all the cookies). I modified my code to remove all the cookies except when the referer is the customize.php page. I haven’t tested it thoroughly yet, but it seems to work.
I had the same problem – problem was with my WP_SITEURL and WP_HOME values in wp-config.php. They were correctly set in the DB, and I used wrong values in the file. After commenting the values in my wp-config.php file, I did not have the problem anymore.
