For instance, if one writes a magazine article or a book that is published using LibreOffice Writer and makes money from it, is this permissible? It is against the license agreement (I believe) of some “writing systems.” Thank you.
It is permitted and I would say even encouraged to do so.
The licence deals only with matters under which terms you can use components of the program to create your own similar (or not) programs, e.g AdamsOffice 
See my detailed answer about license: Is licensing required for isolated usage within an organization?