Is the Washington Post Really Using Us in Bad Faith?

A lot of people on the right actually think that like New York Times and Washington Post reporters are lying to them in their report. What can the media do to regain a degree of trust when basically the objection to them on the right is that they're saying things that these people don't want to hear? "It's not like we really think that the press is biased towards liberals, right? It's more a kind of effort to game the refs"