Problems with deactivating the Private Page Modus

I have built a website that was filled by several people that I have designated as authors. Since the beginning the site runs in “Private Site” mode. If you are logged in everything is running fine and the page is displayed correctly. But as soon as I want to put the website online and remove the login ( uncheck “Private Site”) the page is displayed incorrectly. All pictures and videos are no longer displayed and the scripts are broken when I log out from the admin panel and view the page as a non-registered user. As soon as I have logged in again everything will be displayed correctly! What can be the reason for this?

The website is half a year’s work and now I can’t put it online because I trusted that I can simply turn off the button for “Private Site” and everything is working correctly!

this is a horror scenario and I don’t know what to do! Can you help me?
i have also already tried to disable the plugin, here is the same problem!