I can't point to metrics but the current rash of Washington Post stories seem to be skewing much more left then in the past. It could just be the times we are in a lot of the news I follow seems to be that way.
In the past it may have been a cheap shot, but I think it's fair to say that reality has a left-wing bias right now. Denying climate change is now right-wing orthodoxy and is about to be entrenched in the White House.
Or to put it another way, I think politics has lurched right rather than the Post moving left. Do you have any particular stories in mind, though?