Thanks for the details, I can find the URL, it is layout "Model bearbeiten" ID 765, and the CRED form cell in it:
Inhalt bearbeiten - Erotikmodels ID 766,
In step 4) I can edit the post in in public area, after submit the form, login as an admin user, edit the post again, I can see those checkbox values are saved correctly, there isn't same problem as you mentioned above:
the changes are not made and the settings of the initial entry remain
So it should be a compatibility problem or server problem, we need to check if there is any PHP errors occur in your website, please check these in your website:
1) Deactivate other plugins and switch to wordpress default theme
2) Enable PHP debug mode, and test again, copy and paste the debug logs here
PHP Debugging
In case you think that Types or Views are doing something wrong (what we call a bug), you should enable PHP error logging. Again, edit your wp-config.php file and add the following:
ini_set('log_errors',TRUE);
ini_set('error_reporting', E_ALL);
ini_set('error_log', dirname(__FILE__) . '/error_log.txt');
This will produce a file called ‘error_log.txt’ in your WordPress root directory. Make sure that the web server can create and write this file. If it cannot, use an FTP program to create the file and make it writable to Apache (normally, user www-data).
https://toolset.com/documentation/user-guides/debugging-types-and-views/
3) If the problem still persists, please provide a test site with the same problem, and fill below private detail box with login details and FTP access, I need a live website to test and debug, thanks