The argument is that allegedly he has been quite forceful in them and attempted to shape policy. The Guardian (the newspaper involved) are arguing that it's in the public interest because we should know which direction the monarchy will be going when Charles takes the throne, if indeed he ever does.
I think if it were any other private individual who thought they had enough clout to get the government to change policies (Murdoch? Sugar? ) we would want it brought to public attention. What makes Charles any different?