Generally, fact checking an debooonking is fine, IMO.
Both sides should do it to each other.
It only became fake and gay when partisan organizations were cited as arbiters of truth, the other site defamed and canceled, and generally strong-arming a consensus to force issues into the Zeitgeist.
Remember, nobody is objective. There are people who try to be objective, but you can only trust singular people with that, not organisations.
I tend to trust people more that wear their biases on their sleeve, because they are open with it.
Beware of people who claim to be objective but always bat for the same political team, they are demagogues and charlatans.