<< even if 'objectivity' is self-reflexively posited as an ideal never to be entirely realized in practice. >>
The plain sense seems to be:
*objectivity*: being impartial
*self-reflectively posited*: assumed or asserted by the reporter himself or herself
*an ideal never to be entirely realized in practice*: a standard of perfection that one seeks but that one knows cannot be reached
That is to say, in a first-effort paraphrase: Reporters must try to be impartial, even if they believe that complete impartiality is not possible.