Its attitude, which it has preached and practiced, is skepticism. Now, it finds, the public is applying that skepticism to the press.

Meaning of the quote

The media has long told people to be skeptical and question things. But now, the public is using that same skepticism to question and doubt the media itself. The media's own message of doubt has come back to them, as people are no longer just blindly trusting what the media says.