This is bad news as these fact checkers have proven to be just as biased as any other news souce such sa MSNBC or Fox News. They are fake authorities to decide what is true and what is not. This will lead to ever more tighter group think in the left leaning segments of the society while the right leaning segments will get alienated even further by what they call "mainstream media" institutions. It only takes one false positive identification of "fake news" to discredit this as cencorship by any right leaning person. (And trust me, the bias is there, so the false positive is something that will annoy right leaning people, not left leaning.)
In short: Don't do it. Please. Instead try to work it so that people get exposed to other points of views.