Hmm . . . if you take a look at the image you posted, you'll see that the error message is coming from your Server, not MODX.
Ask the host to double-check the permissions and ownership of this folder in the MODX install:
connectors/system/registry
and the register.php file in that directory.
That said, your symptoms are extremely weird. Login doesn't create or set any System Settings (the Package doesn't even have a script resolver). or menus, and it creates no plugins, so having it installed shouldn't have any effect at all in the Manager.
Login just installs a bunch of chunks and snippets, which are completely inactive in the Manager unless one of the snippets is called on a Manager page (and none are).
Have you implemented the Register snippet? My only thought (other than the file permissions and ownership) is that there's something wrong with the way you're using Register in the front end.
If you're not using Register, it's even weirder, because AFAIK, nothing else accesses that file.
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PLEASE, PLEASE specify the version of MODX you are using.
MODX info for everyone:
http://bobsguides.com/modx.html