Well, we updated to 2.2.14 and the problem persists. So I think it has to do with the server configuration. However, we still can't find the problem. We checked if E_NOTICE errors and display_errors were turned off (they are) and also if the http_host variable is set, it is.
Things we also tried: disabling the .htaccess file, checking the rights of the folder+file that is giving problems (folders 755, file 644), increasing the php memory, overwriting the core files like Susan suggested. Nothing helps.
When we turn display_errors on in the .htaccess file (in hopes of finding the problem) we did find that instead of the POST error (/connectors/security/user.php 500 (Internal Server Error) ) there is a different error in the Firebug panel (and no 500 error):
TypeError: o.result is undefined
https://www.mywebsite.nl/manager/assets/modext/widgets/security/modx.panel.user.js
Line 95
However the POST data in the Firebug console does have the POST info but no answer, so I think it's the same problem.
We're out of ideas for now... Next step is getting help from the host. I'll let you know what happens.