Sure. Nearly all newspapers do that. But they also have their own editorial policies. The Times's Editorial Board is not, to say the very least, supportive of Trump. The NY Post's editorial stance is very pro-Trump, though it, too, occasionally features op-ed pieces critical of him.
And that's how it's always been. On the editorial side, newspapers need not try for impartiality, and very few do. Most newspapers endorse political candidates for the presidency and for some less important offices.
it seems to me that many people have lost sight of the difference between editorials, or opinion pieces, and straight news. In some cases, at a specific paper, the editorial and news departments may have different orientations. For example, the Wall Street Journal's editorial board is quite conservative, though its news department does some excellent investigative reporting that isn't supportive of the current administration.
Within news departments, there are differences. All papers publish some articles that are just straight reporting of an event or action. The author explains what happened, throws in a few quotes from whoever was involved, and that's it. The scope is purely informational. Investigative reporting is different. It examines topics that are controversial, problematic, or in some way mysterious. Investigative reporters dig beneath the surface for information, and they sometimes reach conclusions about what they've found. They do engage in fact checking, as do their bosses, who double check the stories. But unlike editorial or op-ed writers, they don't offer personal opinions.
All of that has always been the case. Forty-five years ago, Woodward and Bernstein were investigative reporters who worked on Watergate, of course. But there is a difference now, and it's provided by the internet. Back then, a newspaper could run only so many stories a day, because of physical limitations. Now, the Times contains a great deal more content than it did in 1973. Most people read it online, and I'd be willing to bet nobody reads all of it. People did read print newspapers in their entirety.
My guess would be that some readers' perception of bias in the Times or any other publication has a good deal to do with what stories come to their attention. And that is affected by how those readers perform searches, and with what stories have more readership than others.
But it's absurd to suggest that newspapers with a "liberal" or "conservative" stance are something new.
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