Yes facts are objective, but when you decide to fact check or not fact check is completely subjective. Fact checking statements out of context can be misleading in themselves, and fact checking statements that were misinterpreted by the fact checkers is also influenced by bias.
Do you remember when the media had a fit about Trump being racist for blocking the flights to countries with high covid rates? How about the two weeks after he announced operation warp speed to develop a vaccine and everybody swore up and down that they wouldn’t take Trump’s vaccine? Trump bears a lot of responsibility for the toxic political culture, but it wasn’t just him.