There's really no way to be "objective" or "unbiased" or whatever we call it these days in the context of political journalism. You can reasonably do a "just the facts" kind of coverage of certain things which at least strives for that, but political coverage these days is so much theater criticism and imagining "how it's going to play" and all sorts of judgments which are only "objective" if you confuse your opinions with facts, which of course is something a lot of people do.
The occasional bad tweet just reaffirms that the bad coverage generally isn't just a mistake, or an attempt to placate conservatives, but a consequence of a worldview which isn't that much different from white nationalists. Years of covering old conservative white people who like Trump (and still like Trump! just checking!) reflects the view that the are the only voters who matter, so much so that minority Americans are excluded. People in the Northeast or the West Coast don't matter. People who live in cities in the South or the Midwest don't matter. Rural minorities don't exist to them, so they don't matter. People who vote for Democrats don't matter.
Real America is what white nationalists say it is, and that drives the political coverage in the NYT and elsewhere.