I recently encountered the idea of reading like a fact-checker, that is, horizontally, by cross-checking a source with other sources (opening additional tabs to do so, thus, "horizontally") rather than vertically in an attempt to determine a source's credibility using only information offered by the source itself. This has now informed how I now teach source assessment to the high school students at my school.
I share vetted sources via class resource pages, a la Libguides, and try to include a brief explanation as to how I concluded such-and-such a source seems credible. I also create brief video tutorials where I think aloud as I assess a particular source and come to a conclusion.
In all this, I try to project an aura of intellectual rigor and distance--I'm looking for the best information, regardless of what my political self might wish were true--leavened with some humor. My hope is to defuse some of the reflexive anger such vetting can stir up, as well as identify how human nature, in the form of, for example, confirmation bias, can unconsciously sabotage our best efforts to become better informed about the world.