I think we have a diversity of press and not a single voice precisely because different outlets are going to cover different things. They must all hew closely to the facts, of course (something some news outlets fail to do all too frequently), but it's okay to choose stories that they think are particularly relevant to their readership. And I don't think it's a secret where the editorial board of the NYTimes has their sympathies in this current government - when even their ostensibly conservative columnists and their entire editorial line is broadly lined up against Trump, no one is going to start reading their stories assuming they come from a place of sympathy for the President or his motives.
I think that if news sources have a clear editorial line but high journalistic standards, people will trust them, and can tell the difference between them and the scourge of fake news. The WaPost might have done the digging to break the Roy Moore story, but they also did their due diligence - and didn't report stories they found fishy or uncorroborated. That's the difference between principled news with a strong editorial bent and 'fake news'.
And this isn't just a liberal phenomenon. There are plenty of right-leaning outlets that also have pretty high journalistic standards - the WSJ is an obvious one. No one has argued that the WSJ doesn't have a strong editorial line, but they also don't automatically distrust news coming from them because - editorial line or not - it's journalism, not propaganda.
If you look at broadcast media - especially cable news - quality and journalistic excellence drop dramatically across the board, though Fox lives in its own unique version of the universe that goes far beyond an editorial slant. But anyone who's getting their news from cable TV might as well be reading a tabloid, so it's no wonder they have low trust in news media.
I really don't think we live in a post-truth era. Yes, people are gullible and they increasingly live in echo chambers due to self-sorting, the internet/social media, etc. - which makes them very susceptible to the kind of manipulations we've seen with fake news. But I really don't think this has been driven by a wholesale rejection of high quality journalism with an editorial slant; most people didn't even start consuming any decent media, so they don't even know the difference. All that's happened is that it's easier to access and target people with crazy shit they're likely to believe. It shouldn't take away from the important role of careful curation and editing of news meeting high journalistic standards to serve the public good.