I tried to enable the cache as you say but the result is the same it appears the invalid token message and es mobile does not work ..
It seems like i also hitting this issue even i excluded your homepage menu item from that plugin.
For now I've temporary disable this cache plugin since it always cached those login token on the page, this is what i referring that login token
http://take.ms/mu4Vm .
Perhaps you can consider change to use pagespeed to optimise your site from your server, it's actually an apache / nginx module that can be used to compress and minify a page on the web server's layer without compromising performance of php, so it will improve your site performance faster as well.
Then enabled Gzip compression from backend, it will reduces/optimise for those site image, javascript and css resources file size on your site.
You can read more about mod_pagespeed from
https://developers.google.com/speed/pagespeed/module/
Hope this suggestion will help.
i istalled the plugin "JCH Optimize " now is disable , yuo can check it
It seems work fine for me when i enabled it, perhaps you can clear your browser cache and see how it goes?