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I could resolve the problem.
I compared the database from my 2nd development environment with database from the live system and noticed that the fields and content of the table "GDN_Permission" were different.
I have created the state of the database of the 2nd system on the live system now. Since then the sitemap works.
Check the permissions for Guests and Members.
Go to Dashboard -> Users, Roles & Permissions -> Edit Guest or Member
Untick "View" in the category you want to hide.
I've already figured out the correlation between the config.php entry and the code c("X.Y.Z",'some default value').