Also the CSS around the site is broken. For instance: http://imgur.com/a/XlFp7 vs http://imgur.com/a/ZmEq4. The blue box in the bottom has a wrong padding, font sizes are different etc. But it is all affected by the cache bug, because once logged in it all works.
Thank you. Yes chat seems to be back again. The problem is WP rocket indeed, when logged in the site works perfectly. So something with HWP affects the cache. Okay thank you so much for looking into it!